ch03_Descriptive_Statistics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computational Statistics for Data Analysis\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <div class=\"alert alert-error\"><strong><center><small>\"Statistics is the discipline of using data samples to support claims about populations.\"<small></center></strong> </div>\n",
    "\n",
    "In this notebook, we will get familiar with Descriptive statistics that comprise  concepts, terms, measures and tools that help to describe, show and summarize the data in a meaningful way. When analysing data, such as the price of flats renting per year, it is possible to use both descriptive and inferential statistics in order to analyse the results and draw some conclusions. We will discuss basic concepts,  terms and procedures, like mean, median, variance, correlation, etc.,  to explore, describe and summarize the given set of data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Statistics is based on 2 main concepts:\n",
    "\n",
    "* A **population** is a collection of objects, items (“units”) about which information is sought.\n",
    "\n",
    "* A **sample** is a part of the population that is observed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'>\n",
    "# 1 Descriptive Statistics.\n",
    "* 1.1 Getting data\n",
    "* 1.2 Data preparation\n",
    "* 1.3 Improving data as a pandas DataFrame\n",
    "* 1.4 Data cleaning \n",
    " <font\\>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### \"Are the men more likely to become high income professionals i.e. to receive income bigger than 50K?\"\n",
    "\n",
    "Some people believe it is true, but **without data analysis** to support it, this claim is a case of **anecdotal evidence**:\n",
    "\n",
    "* There are a **small number of samples** (personal experience, friends, etc.).\n",
    "* There is a **selection bias**: most *believers* are interested in this claim because their first babies were late.\n",
    "* There is a **confirmation bias**: believers might be more likely to contribute data that confirm it.\n",
    "* Sources are **innaccurate**: personal stories are subject to memory deformations. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Getting Data\n",
    "\n",
    "Let us consider a public database, called “Adult” dataset hosted on the UCI’s Machine Learning Repository (https://archive.ics.uci.edu/ml/datasets/Adult), that contains approximately 32.000 observations about different financial parameters of US population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Data preparation\n",
    "\n",
    "One of the reasons we are using a general-purpose language such as Python rather than a stats language like R is that for many projects the *hard* part is preparing the data, not doing the analysis.\n",
    "\n",
    "The most common steps are:\n",
    "\n",
    "1. **Getting the data**. Data can be directly read from a file or it might be necessary to scrap the web.\n",
    "2. **Parsing the data**.  Of course, this depends on what format it is in: plain text, fixed columns, CSV, XML, HTML, etc.\n",
    "3. **Cleaning the data**.  Survey responses and other data files are almost always incomplete.  Sometimes there are multiple codes for things like, *not asked*, *did not know*, and *declined to answer*. And there are almost always errors. A simple strategy is to remove or ignore incomplete records.\n",
    "4. **Building data structures**. Once you read the data, you usually want to store it in a data structure that lends itself to the analysis you want to do.\n",
    "\n",
    "If the data fits into memory, building a data structure is usually the way to go.   If not, you could build a database, which is an out-of-memory data structure. Most databases provide a mapping from keys to values, so they are like dictionaries.\n",
    "\n",
    "Let us read the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "file = open('files/ch03/adult.data', 'r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def chr_int(a):\n",
    "    if a.isdigit():\n",
    "        return int(a)\n",
    "    else:\n",
    "        return 0\n",
    "                \n",
    "data=[]\n",
    "for line in file:\n",
    "    data1=line.split(', ')\n",
    "    if len(data1)==15:\n",
    "        data.append([chr_int(data1[0]),data1[1],chr_int(data1[2]),data1[3],chr_int(data1[4]),data1[5],data1[6],\\\n",
    "            data1[7],data1[8],data1[9],chr_int(data1[10]),chr_int(data1[11]),chr_int(data1[12]),data1[13],\\\n",
    "            data1[14]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[50, 'Self-emp-not-inc', 83311, 'Bachelors', 13, 'Married-civ-spouse', 'Exec-managerial', 'Husband', 'White', 'Male', 0, 0, 13, 'United-States', '<=50K\\n']]\n"
     ]
    }
   ],
   "source": [
    "print(data[1:2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Importing data as a pandas DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>type_employer</th>\n",
       "      <th>fnlwgt</th>\n",
       "      <th>education</th>\n",
       "      <th>education_num</th>\n",
       "      <th>marital</th>\n",
       "      <th>occupation</th>\n",
       "      <th>relationship</th>\n",
       "      <th>race</th>\n",
       "      <th>sex</th>\n",
       "      <th>capital_gain</th>\n",
       "      <th>capital_loss</th>\n",
       "      <th>hr_per_week</th>\n",
       "      <th>country</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>39</td>\n",
       "      <td>State-gov</td>\n",
       "      <td>77516</td>\n",
       "      <td>Bachelors</td>\n",
       "      <td>13</td>\n",
       "      <td>Never-married</td>\n",
       "      <td>Adm-clerical</td>\n",
       "      <td>Not-in-family</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>2174</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50</td>\n",
       "      <td>Self-emp-not-inc</td>\n",
       "      <td>83311</td>\n",
       "      <td>Bachelors</td>\n",
       "      <td>13</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Exec-managerial</td>\n",
       "      <td>Husband</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>13</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>38</td>\n",
       "      <td>Private</td>\n",
       "      <td>215646</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Divorced</td>\n",
       "      <td>Handlers-cleaners</td>\n",
       "      <td>Not-in-family</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>53</td>\n",
       "      <td>Private</td>\n",
       "      <td>234721</td>\n",
       "      <td>11th</td>\n",
       "      <td>7</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Handlers-cleaners</td>\n",
       "      <td>Husband</td>\n",
       "      <td>Black</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>28</td>\n",
       "      <td>Private</td>\n",
       "      <td>338409</td>\n",
       "      <td>Bachelors</td>\n",
       "      <td>13</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Prof-specialty</td>\n",
       "      <td>Wife</td>\n",
       "      <td>Black</td>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>Cuba</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age     type_employer  fnlwgt  education  education_num  \\\n",
       "0   39         State-gov   77516  Bachelors             13   \n",
       "1   50  Self-emp-not-inc   83311  Bachelors             13   \n",
       "2   38           Private  215646    HS-grad              9   \n",
       "3   53           Private  234721       11th              7   \n",
       "4   28           Private  338409  Bachelors             13   \n",
       "\n",
       "              marital         occupation   relationship   race     sex  \\\n",
       "0       Never-married       Adm-clerical  Not-in-family  White    Male   \n",
       "1  Married-civ-spouse    Exec-managerial        Husband  White    Male   \n",
       "2            Divorced  Handlers-cleaners  Not-in-family  White    Male   \n",
       "3  Married-civ-spouse  Handlers-cleaners        Husband  Black    Male   \n",
       "4  Married-civ-spouse     Prof-specialty           Wife  Black  Female   \n",
       "\n",
       "   capital_gain  capital_loss  hr_per_week        country   income  \n",
       "0          2174             0           40  United-States  <=50K\\n  \n",
       "1             0             0           13  United-States  <=50K\\n  \n",
       "2             0             0           40  United-States  <=50K\\n  \n",
       "3             0             0           40  United-States  <=50K\\n  \n",
       "4             0             0           40           Cuba  <=50K\\n  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame(data) #  Two-dimensional size-mutable, potentially heterogeneous tabular data structure with labeled axes \n",
    "\n",
    "df.columns = ['age', 'type_employer', 'fnlwgt', 'education', \n",
    "                \"education_num\",\"marital\", \"occupation\", \"relationship\", \"race\",\"sex\",\n",
    "                \"capital_gain\", \"capital_loss\", \"hr_per_week\",\"country\",\"income\"]\n",
    "df.head()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>type_employer</th>\n",
       "      <th>fnlwgt</th>\n",
       "      <th>education</th>\n",
       "      <th>education_num</th>\n",
       "      <th>marital</th>\n",
       "      <th>occupation</th>\n",
       "      <th>relationship</th>\n",
       "      <th>race</th>\n",
       "      <th>sex</th>\n",
       "      <th>capital_gain</th>\n",
       "      <th>capital_loss</th>\n",
       "      <th>hr_per_week</th>\n",
       "      <th>country</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>32556</th>\n",
       "      <td>27</td>\n",
       "      <td>Private</td>\n",
       "      <td>257302</td>\n",
       "      <td>Assoc-acdm</td>\n",
       "      <td>12</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Tech-support</td>\n",
       "      <td>Wife</td>\n",
       "      <td>White</td>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>38</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32557</th>\n",
       "      <td>40</td>\n",
       "      <td>Private</td>\n",
       "      <td>154374</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Machine-op-inspct</td>\n",
       "      <td>Husband</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&gt;50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32558</th>\n",
       "      <td>58</td>\n",
       "      <td>Private</td>\n",
       "      <td>151910</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Widowed</td>\n",
       "      <td>Adm-clerical</td>\n",
       "      <td>Unmarried</td>\n",
       "      <td>White</td>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32559</th>\n",
       "      <td>22</td>\n",
       "      <td>Private</td>\n",
       "      <td>201490</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Never-married</td>\n",
       "      <td>Adm-clerical</td>\n",
       "      <td>Own-child</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32560</th>\n",
       "      <td>52</td>\n",
       "      <td>Self-emp-inc</td>\n",
       "      <td>287927</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Exec-managerial</td>\n",
       "      <td>Wife</td>\n",
       "      <td>White</td>\n",
       "      <td>Female</td>\n",
       "      <td>15024</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&gt;50K\\n</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       age type_employer  fnlwgt   education  education_num  \\\n",
       "32556   27       Private  257302  Assoc-acdm             12   \n",
       "32557   40       Private  154374     HS-grad              9   \n",
       "32558   58       Private  151910     HS-grad              9   \n",
       "32559   22       Private  201490     HS-grad              9   \n",
       "32560   52  Self-emp-inc  287927     HS-grad              9   \n",
       "\n",
       "                  marital         occupation relationship   race     sex  \\\n",
       "32556  Married-civ-spouse       Tech-support         Wife  White  Female   \n",
       "32557  Married-civ-spouse  Machine-op-inspct      Husband  White    Male   \n",
       "32558             Widowed       Adm-clerical    Unmarried  White  Female   \n",
       "32559       Never-married       Adm-clerical    Own-child  White    Male   \n",
       "32560  Married-civ-spouse    Exec-managerial         Wife  White  Female   \n",
       "\n",
       "       capital_gain  capital_loss  hr_per_week        country   income  \n",
       "32556             0             0           38  United-States  <=50K\\n  \n",
       "32557             0             0           40  United-States   >50K\\n  \n",
       "32558             0             0           40  United-States  <=50K\\n  \n",
       "32559             0             0           20  United-States  <=50K\\n  \n",
       "32560         15024             0           40  United-States   >50K\\n  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32561, 15)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's count the number of items per country:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "country\n",
      "?                               583\n",
      "Cambodia                         19\n",
      "Canada                          121\n",
      "China                            75\n",
      "Columbia                         59\n",
      "Cuba                             95\n",
      "Dominican-Republic               70\n",
      "Ecuador                          28\n",
      "El-Salvador                     106\n",
      "England                          90\n",
      "France                           29\n",
      "Germany                         137\n",
      "Greece                           29\n",
      "Guatemala                        64\n",
      "Haiti                            44\n",
      "Holand-Netherlands                1\n",
      "Honduras                         13\n",
      "Hong                             20\n",
      "Hungary                          13\n",
      "India                           100\n",
      "Iran                             43\n",
      "Ireland                          24\n",
      "Italy                            73\n",
      "Jamaica                          81\n",
      "Japan                            62\n",
      "Laos                             18\n",
      "Mexico                          643\n",
      "Nicaragua                        34\n",
      "Outlying-US(Guam-USVI-etc)       14\n",
      "Peru                             31\n",
      "Philippines                     198\n",
      "Poland                           60\n",
      "Portugal                         37\n",
      "Puerto-Rico                     114\n",
      "Scotland                         12\n",
      "South                            80\n",
      "Taiwan                           51\n",
      "Thailand                         18\n",
      "Trinadad&Tobago                  19\n",
      "United-States                 29170\n",
      "Vietnam                          67\n",
      "Yugoslavia                       16\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "counts = df.groupby('country').size()\n",
    "\n",
    "print(counts) \n",
    "# also: df.outcome.value_counts()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "age\n",
      "17    395\n",
      "18    550\n",
      "19    712\n",
      "20    753\n",
      "21    720\n",
      "     ... \n",
      "85      3\n",
      "86      1\n",
      "87      1\n",
      "88      3\n",
      "90     43\n",
      "Length: 73, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "counts = df.groupby('age').size() # grouping by age\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21790, 15)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml = df[(df.sex == 'Male')] # grouping by sex\n",
    "ml.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6662, 15)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml1 = df[(df.sex == 'Male')&(df.income=='>50K\\n')]\n",
    "ml1.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's separate male from female according to the income. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10771, 15)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm =df[(df.sex == 'Female')]\n",
    "fm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1179, 15)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm1 =df[(df.sex == 'Female')&(df.income=='>50K\\n')]\n",
    "fm1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The rate of people with high income is:  24 %.\n",
      "The rate of men with high income is:  30 %.\n",
      "The rate of women with high income is:  10 %.\n"
     ]
    }
   ],
   "source": [
    "df1=df[(df.income=='>50K\\n')]\n",
    "\n",
    "print('The rate of people with high income is: ', int(len(df1)/float(len(df))*100), '%.') \n",
    "print('The rate of men with high income is: ', int(len(ml1)/float(len(ml))*100), '%.' )\n",
    "print('The rate of women with high income is: ', int(len(fm1)/float(len(fm))*100), '%.' )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Data Cleaning\n",
    "\n",
    "The most common steps are:\n",
    "\n",
    "+ **Sample the data**. If the amount of raw data is huge, processing all of them may require an extensive amount of processing power which may not be practical.  In this case, it is quite common to sample the input data to reduce the size of data that need to be processed.\n",
    "\n",
    "+ **Impute missing data**. It is quite common that some of the input records are incomplete in the sense that certain fields are missing or have input error.  In a typical tabular data format, we need to validate each record contains the same number of fields and each field contains the data type we expect. In case the record has some fields missing, we have the following choices: \n",
    "<small>\n",
    "* (a) Discard the whole record if it is incomplete; \n",
    "* (b) Infer the missing value based on the data from other records.  A common approach is to fill the missing data with the average, or the median.\n",
    "<small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ **Normalize numeric value**. Normalize data is about transforming numeric data into a uniform range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ **Reduce dimensionality**. High dimensionality can be a problem for some machine learning methods.  There are two ways to reduce the number of input features.  One is about $removing$ $irrelevant$ input variables, another one is about $removing$ $redundant$ input variables.\n",
    "+ **Add derived features**. In some cases, we may need to compute additional attributes from existing attributes (f.e. converting a geo-location to a zip code, or converting the age to an age group).\n",
    "+ **Discretize numeric value into categories**. Discretize data is about cutting a continuous value into ranges and assigning the numeric with the corresponding bucket of the range it falls on.  For numeric attribute, a common way to generalize it is to discretize it into ranges, which can be either constant width (variable height/frequency) or variable width (constant height).\n",
    "+ **Binarize categorical attributes**. Certain machine learning models only take binary input (or numeric input).  In this case, we need to convert categorical attribute into multiple binary attributes, while each binary attribute corresponds to a particular value of the category. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ **Select, combine, aggregate data**. Designing the form of training data is the most important part of the whole predictive modeling exercise because the accuracy largely depends on whether the input features are structured in an appropriate form that provide strong signals to the learning algorithm. Rather than using the raw data as it is, it is quite common that multiple pieces of raw data need to be combined together, or aggregating multiple raw data records along some dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Exploratory Data Analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Summarizing the data: \n",
    "#### 2.1.1 Sample Mean \n",
    "\n",
    "If you have a sample of $n$ values, $x_i$, the **sample mean** is the sum of the values divided by the number of values:\n",
    "\n",
    "$$ \\mu = \\frac{1}{n} \\sum_i x_i$$\n",
    "\n",
    "The **mean** is the most basic and important summary statistic. It describes the central tendency of a sample. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a small difference!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average age of men is:  39.43354749885268 .\n",
      "The average age of women is:  36.85823043357163 .\n"
     ]
    }
   ],
   "source": [
    "print('The average age of men is: ', ml['age'].mean(), '.' )\n",
    "print('The average age of women is: ', fm['age'].mean(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This difference in sample means can be considered a first evidence of our hypothesis!\n",
    "\n",
    "\n",
    "**Comment: ** *Later, we will work with both concepts: the population mean and the sample mean. Do not confuse them! Remember, the first one is the mean of samples taken from the population and the second one is the mean of the whole population.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average age of high-income men is:  44.62578805163614 .\n",
      "The average age of high-income women is:  42.125530110262936 .\n"
     ]
    }
   ],
   "source": [
    "print('The average age of high-income men is: ', ml1['age'].mean(), '.' )\n",
    "print('The average age of high-income women is: ', fm1['age'].mean(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1.2 Sample Variance\n",
    "\n",
    "Usually, mean is not a sufficient descriptor of the data, we can do a little better with two numbers: mean and **variance**:\n",
    "\n",
    "$$ \\sigma^2 = \\frac{1}{n} \\sum_i (x_i - \\mu)^2 $$\n",
    "\n",
    "**Variance** $\\sigma^2$ describes the *spread* of data. The term $(x_i - \\mu)$ is called the *deviation from the mean*, so variance is the mean squared deviation.\n",
    "\n",
    "The square root of variance, $\\sigma$, is called the **standard deviation**. We define standard deviation because variance is hard to interpret (in the case the units are grams, the variance is in grams squared). Let's get the basic statistics for our example data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics of age for men: mu: 39.43354749885268 var: 178.77375174530096 std: 13.37063019252649\n",
      "Statistics of age for women: mu: 36.85823043357163 var: 196.3837063948037 std: 14.01369709943824\n"
     ]
    }
   ],
   "source": [
    "ml_mu = ml['age'].mean()\n",
    "fm_mu = fm['age'].mean()\n",
    "ml_var = ml['age'].var()\n",
    "fm_var = fm['age'].var()\n",
    "ml_std = ml['age'].std()\n",
    "fm_std = fm['age'].std()\n",
    "print('Statistics of age for men: mu:', ml_mu, 'var:', ml_var, 'std:', ml_std)\n",
    "print('Statistics of age for women: mu:', fm_mu, 'var:', fm_var, 'std:', fm_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics of hours per week for men: mu: 42.42808627810923 var: 146.88846717142022 std: 12.119755243874367\n",
      "Statistics  of hours per week for women: mu: 36.410361154953115 var: 139.50679700047252 std: 11.81129954748725\n"
     ]
    }
   ],
   "source": [
    "ml_mu_hr = ml['hr_per_week'].mean()\n",
    "fm_mu_hr = fm['hr_per_week'].mean()\n",
    "ml_var_hr = ml['hr_per_week'].var()\n",
    "fm_var_hr = fm['hr_per_week'].var()\n",
    "ml_std_hr = ml['hr_per_week'].std()\n",
    "fm_std_hr = fm['hr_per_week'].std()\n",
    "print('Statistics of hours per week for men: mu:', ml_mu_hr, 'var:', ml_var_hr, 'std:', ml_std_hr)\n",
    "print('Statistics  of hours per week for women: mu:', fm_mu_hr, 'var:', fm_var_hr, 'std:', fm_std_hr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1.3 Sample Median\n",
    "\n",
    "The statistical median is an order statistic that gives the *middle* value of a sample. It is a value more robust to ouliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median age per men and women:  38.0 35.0\n",
      "Median age per men and women with high-income:  44.0 41.0\n"
     ]
    }
   ],
   "source": [
    "ml_median= ml['age'].median()\n",
    "fm_median= fm['age'].median()\n",
    "print(\"Median age per men and women: \", ml_median, fm_median)\n",
    "\n",
    "ml_median_age= ml1['age'].median()\n",
    "fm_median_age= fm1['age'].median()\n",
    "print(\"Median age per men and women with high-income: \", ml_median_age, fm_median_age)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median hours per week per men and women:  40.0 40.0\n"
     ]
    }
   ],
   "source": [
    "ml_median_hr= ml['hr_per_week'].median()\n",
    "fm_median_hr= fm['hr_per_week'].median()\n",
    "print(\"Median hours per week per men and women: \", ml_median_hr, fm_median_hr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1.4 Summarizing the data: Quantiles & Percentiles\n",
    "\n",
    "Order the sample $\\{ x_i \\}$, then find $x_p$ so that it divides the data into two parts where:\n",
    "\n",
    "+ a fraction $p$ of the data values are less than or equal to $x_p$ and\n",
    "+ the remaining fraction $(1 − p)$ are greater than $x_p$.\n",
    "\n",
    "That value $x_p$ is the pth-quantile, or 100×pth percentile.\n",
    "\n",
    "**5-number summary**: $x_{min}, Q_1, Q_2, Q_3, x_{max}$, where $Q_1$ is the 25×pth percentile,\n",
    "$Q_2$ is the 50×pth percentile and $Q_3$ is the 75×pth percentile."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most common representation of a distribution is a **histogram**, which is a graph that shows the frequency of each value. Let us visualize the histogram for the age of the male and female populations in our example: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAAELCAYAAAD3HtBMAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAcYUlEQVR4nO3df7xVdZ3v8dd70FGU/BV5BgEHe4SVSpmQMbfJe1BvkTphTj/wWsnYxExZk8XthvXIfj0cqZv2y7Sh8Kplnqg0GdOKUMaph2bg2ACSIwVXQYSxHyJqFPi5f3y/p/YcN4d11ll777U57+fjsR977+9aa+/3wYMf1ve71veriMDMzGyo/qTTAczMrDu5gJiZWSkuIGZmVooLiJmZleICYmZmpezT6QDtNHbs2Jg0aVJbvuuJJ57gwAMPbMt3DYdzVqsbcnZDRnDOKg0348qVKx+NiOc8Y0NEjJjH1KlTo11uv/32tn3XcDhntbohZzdkjHDOKg03I7Aimvw/1V1YZmZWiguImZmV0tYCImmipNslrZW0RtK7c/tHJG2SdG9+nNZwzIWS1km6X9KrGtqnSlqVt31Oktr5s5iZjXTtHkTfCcyLiHskPQtYKWlp3vbpiPhU486SjgFmA8cCRwA/kHR0ROwCrgTmAncBtwAzgVvb9HOYmY14bT0DiYjNEXFPfv04sBYYP8ghs4C+iNgREeuBdcCJksYBB0XEnXmA51rgzNamNzOzRooOTaYoaRJwB3Ac8F5gDrANWEE6S/m1pMuBuyLiq/mYRaSzjA3Agog4Nbe/Anh/RJzR5Hvmks5U6OnpmdrX19faHyzbvn07Y8aMact3DYdzVqsbcnZDRnDOKg0344wZM1ZGxLRnbGh2aVarH8AYYCVwVn7fA4winRFdDFyV278AvKnhuEXAXwMvBX7Q0P4K4J/39L2+jPeZnLNa3ZCzGzJGOGeV9prLeCXtC3wLuC4ibgCIiC0RsSsinga+BJyYd98ITGw4fALwcG6f0KTdzMzapN1XYYl0FrE2Ii5raB/XsNtrgdX59RJgtqT9JB0FTAbujojNwOOSpufPfAtwU1t+CDMzA9p/FdbLgTcDqyTdm9s+AJwt6XggSOMbfwcQEWskLQbuI13BdX6kK7AA3g5cDYwmjYv4CqyKTZr/ndLHblhweoVJzKyO2lpAIuKHQLP7NW4Z5JiLSeMiA9tXkAbgzcysA3wnupmZleICYmZmpbiAmJlZKS4gZmZWiguImZmV4gJiZmaluICYmVkpLiBmZlaKC4iZmZXiAmJmZqW4gJiZWSntnkzR2mxPEyLOm7KTOcOYNNHMRi6fgZiZWSkuIGZmVooLiJmZleICYmZmpbiAmJlZKb4Ky2qn2ZVjRa8W81K6Zu3jMxAzMyvFBcTMzEpxATEzs1JcQMzMrBQXEDMzK8UFxMzMSnEBMTOzUlxAzMysFBcQMzMrxQXEzMxKcQExM7NSPBeW7VX2tALjnnguLbPifAZiZmaluICYmVkpLiBmZlZKWwuIpImSbpe0VtIaSe/O7YdJWirpgfx8aMMxF0paJ+l+Sa9qaJ8qaVXe9jlJaufPYmY20rX7DGQnMC8iXghMB86XdAwwH1gWEZOBZfk9edts4FhgJnCFpFH5s64E5gKT82NmO38QM7ORrq0FJCI2R8Q9+fXjwFpgPDALuCbvdg1wZn49C+iLiB0RsR5YB5woaRxwUETcGREBXNtwjJmZtYHS/3878MXSJOAO4DjgwYg4pGHbryPiUEmXA3dFxFdz+yLgVmADsCAiTs3trwDeHxFnNPmeuaQzFXp6eqb29fW18sf6g+3btzNmzJi2fNdgVm16bNDtPaNhy1PVf++U8QeXPrZZ5lblHGg4uaE+/90H0w0ZwTmrNNyMM2bMWBkR0wa2d+Q+EEljgG8BF0TEtkGGL5ptiEHan9kYsRBYCDBt2rTo7e0dct4yli9fTru+azB7Wkd83pSdXLqq+l+DDef0lj62WeZW5RxoOLmhPv/dB9MNGcE5q9SqjG2/CkvSvqTicV1E3JCbt+RuKfLz1ty+EZjYcPgE4OHcPqFJu5mZtUm7r8ISsAhYGxGXNWxaApybX58L3NTQPlvSfpKOIg2W3x0Rm4HHJU3Pn/mWhmPMzKwN2t2F9XLgzcAqSffmtg8AC4DFkt4KPAi8HiAi1khaDNxHuoLr/IjYlY97O3A1MJo0LnJrm34GMzOjzQUkIn5I8/ELgFN2c8zFwMVN2leQBuDNzKwDfCe6mZmV4gJiZmaluICYmVkpLiBmZlaKC4iZmZVS6CosSfsAoyJiR0PbK4FjgDv657cyM7ORo+hlvF8HHgPOA5D0D8BngB3AKElnRcTNLUloZma1VLQLazpwS8P79wGXRsRo4MvAB6sOZmZm9Vb0DOTZwCMAkqYARwBfzNu+AZxTfTTrZpP2MImjmXW/ogVkCzAJ+CFp4ab/FxE/z9tGA09XH23vMZz/mW5YcHqFSczMqlO0gHwD+ISkFwN/A1zesO0lwANVBzMzs3orWkDmA9uAl5KWkr2kYdtU0iC7mZmNIIUKSETsBD62m21nVZrIzMy6wpBuJJT0akkfkrRQ0pG57SRJR7QmnpmZ1VXRGwl7SIs7TSWtR34U6SqsB0ljIr8lrc9hZmYjRNEzkM8DY4AX5Efjmh4/YDdreZiZ2d6r6CD6TODciFgnadSAbRuB8dXGMjOzuhvKGMiu3bSPBZ6qIIuZmXWRogXkX4F3DTj7iPx8HnBbpanMzKz2inZhvZ90F/pq4EZS8XibpONI65JPb008MzOrq0JnIBGxmnQF1gpgDqk76yzgIeBlEfEfrQpoZmb1VPQMhDz31ZtbmMXMzLqIVyQ0M7NSdnsGImnxED4nIuKNFeQxM7MuMVgX1nPalsLMzLrObgtIRMxoZxAzM+suHgMxM7NSChcQSVMkfU3SOklP5OevSXpRKwOamVk9FZ2N90xgMfBz4JvAVuBwYBawQtIbIuLbLcpoZmY1VPQ+kE8ANwFviIj+KUyQdCGpoHwS+Hbl6czMrLaKdmFNBL7cWDwgXbsLLAQmVB3MzMzqregZyArgWOB7TbYdB9xTWSL7LybN/06nI5iZNVW0gLwX6JO0L6mrqn8M5LXA3wKzJR3Qv3NEPFlxTrPamzT/O8ybspM5JYr+hgWntyCRWWsV7cK6G3gucAlwH/Bofv7H3P5j4PGGR1OSrpK0VdLqhraPSNok6d78OK1h24X5aq/7Jb2qoX2qpFV52+ckaeB3mZlZaxU9AzmPP67/MRxXA5cD1w5o/3REfKqxQdIxwGxS19kRwA8kHR0Ru4ArgbnAXcAtpBUTb60gn5mZFVSogETE1VV8WUTcIWlSwd1nAX0RsQNYL2kdcKKkDcBBEXEngKRrgTNxATEzaysNuLCq9V+YCsjNEXFcfv8R0hoj20iD9fMi4teSLgfuioiv5v0WkYrEBmBBRJya218BvD8iztjN980lna3Q09Mzta+vr2U/W6Pt27czZswYAFZteqwt31lGz2jY0gULErcr55TxB5c+dtWmx0rnHM73DlXj72adOWd1hptxxowZKyNi2sD2ojcS/ilwAWnQfDyw/8B9IuLwktmuBD5O6iL7OHApqcus2bhGDNLeVEQsJF1qzLRp06K3t7dkzKFZvnw5/d9VZlC1XeZN2cmlqwovC9Mx7cq54Zze0sfOyYPoZXIO53uHqvF3s86cszqtylj0N/1K4BzSzYS3Ab+rKkBEbOl/LelLwM357UbS/Sf9JgAP5/YJTdrNzKyNihaQs4ALIuKLVQeQNC4iNue3ryWtuw6wBPiapMtIg+iTgbsjYpekxyVNJ1399Rbg81XnMjOzwRUtIL8CHhzul0m6HugFxkraCHwY6JV0PKkbagPwdwARsSYvanUfsBM4P1+BBfB20hVdo0njIh5ANzNrs6IF5GPAPEn/EhFPlP2yiDi7SfOiQfa/GLi4SfsK0h3wZmbWIUUv470m35fxoKSVwG+euYuXtDUzG0mKXoU1D3gf8AhwILBvK0OZmVn9Fe3Cmg98DnjPwBl5zcxsZCo6F5ZIN/+5eJiZGVC8gFwN/HULc5iZWZcp2oW1EXivpB+QbiT8zYDtERFXVhnMzMzqrWgBuSw/TwBObrI9SHerm5nZCFH0Mt6iXV1mZjZCuDCYmVkpQ5o2VNIE4Giaz8Z7S1WhzMys/oreSPgsYDHwyv6m/Nx4We+oCnOZmVnNFe3CugQ4EngFqXi8ljQp4iJgPTC9FeHMzKy+ihaQ00iTGv44v384Iu6IiLmkNULe14pwZmZWX0XHQHqAh/JaHE8AhzVsuwX4VuXJzDpgUo1XjzSrm6JnIA8BY/PrB4DG9cdfBvy2ylBmZlZ/Rc9AlgKnAjcCnwaukTQV2AGcRFrH3MzMRpCiBeT9wAEAEfEVSduB15FWBHwn8E+tiVcfQ+3amDdlJ3PcHWJme7Gid6I/CTzZ8P5G0tmImZmNUIXGQCQdLumohveSNFfSZyT9VevimZlZXQ1lOvf3NLz/KHAFMBO4UdKcamOZmVndFS0gJ5CmcUfSnwBvBz4QES8g3R9yQUvSmZlZbRUtIAcDv8yvp5LuA7kuv78NeF7FuczMrOaKFpCNwDH59enAzyJiU35/ML4PxMxsxCl6Ge9VwCclnUoqIBc2bJsOrK06mJmZ1VvRy3gvkbQJeCnwLlJB6XcY8OUWZDMzsxorvB5IRFwLXNuk/e8rTWRmZl1hSAtKmVlrDGcSxw0LTq8wiVlxXtLWzMxKcQExM7NSXEDMzKwUFxAzMyulcAGR9CJJX5f0c0k7JJ2Q2y+W9OrWRTQzszoqOhvvq4GVwJ+RLuXdt2HzDtK9IWZmNoIUPQO5BLg6Iv47afLERvcCxxf5EElXSdoqaXVD22GSlkp6ID8f2rDtQknrJN0v6VUN7VMlrcrbPidJBX8OMzOrSNEC8gLg6/l1DNi2jXQ3ehFXk6aAbzQfWBYRk4Fl+T2SjgFmA8fmY66QNCofcyUwF5icHwM/08zMWqxoAdkKPHc3244FHizyIRFxB/CrAc2zgGvy62uAMxva+yJiR0SsB9YBJ0oaBxwUEXdGRJC61M7EzMzaquid6H3AxyTdB9yZ20LS0aT10hcNI0NPRGwGiIjNkg7P7eOBuxr225jbfp9fD2xvStJc0tkKPT09LF++vFTIeVN2Dmn/ntFDP6YTnLNancg51N/p7du3l/570E7OWZ1WZSxaQD5Ems79X4BHcttNpEH17wP/WHkyaDauEYO0NxURC4GFANOmTYve3t5SYeYMcaqJeVN2cumq+s8U45zV6kTODef0Dmn/5cuXU/bvQTs5Z3ValbHobLw7gDMknQKcAowldUUti4ilw8ywRdK4fPYxjtRdBunMYmLDfhOAh3P7hCbtZmbWRkP6p1JELCMNdFdpCXAusCA/39TQ/jVJlwFHkAbL746IXZIelzQd+DHwFuDzFWcyM7M92G0BkXTAUD4oIp7c0z6Srgd6gbGSNgIfJhWOxZLeShqMf33+vDWSFgP3ATuB8yNiV/6ot5Ou6BoN3JofZmbWRoOdgWxnkLGFJkbtaYeIOHs3m07Zzf4X88z7ToiIFcBxQ8hmZmYVG6yAnMfQCoiZmY0guy0gEXF1G3OYmVmX8Wy8ZmZWSuGrsCS9EXgbcDSw/8DtEXH4Mw4yM7O9VtHZeP8naZqRdaT7LpYAN+fjtwGXtyqgmZnVU9EurPcBHwfOz++viIjzgKOAR4E9XsJrZmZ7l6IFZDLwo3wfxi7gIICIeBz4BPDO1sQzM7O6KlpAHgP2y683AS9s2Cbg2VWGMjOz+is6iL4CeBHwPdL4x0WSdgK/Ay4iTSliZmYjSNECcgnw5/n1Rfn1FaS7z39Cni7dzMxGjqKz8d5FXpsjIn4DzJK0H7BfRGxrXTwzM6ur0gsX5Cned1SYxczMushgs/FeNITPiYj4eAV5zMysSwx2BvIR4CngCZqvAtgoSPeJmJnZCDFYAfkFcCSwkrQm+o0e7zAzs36Dzcb7PEnTgNmks4srJX0XuB64OSKealNGMxvEpPnfGdL+86bsZE7DMRsWnF51JBshBr2RMCJWRMT/iogjgZnAI6R5r7ZKuk7SSe0IaWZm9VN4OveIuCMi3gFMBL4IvBG4oEW5zMys5oYynfvLSd1ZrwOeBXwTuLJFuczMrOYGLSCSTiAVjTcCPcB3gfcASyLCM/CamY1gg90Hcj9puvbbgA8DN/gqLLO9z1AH4Rt5AH5kG+wMZDLwW2AqcALwSWn3t4N4RUIzs5FlsALy0balMDOzrjPYfSAuIGZmtluFL+M1MzNr5AJiZmaluICYmVkpLiBmZlaKC4iZmZXiAmJmZqW4gJiZWSkuIGZmVooLiJmZlVKbAiJpg6RVku6VtCK3HSZpqaQH8vOhDftfKGmdpPslvapzyc3MRqbaFJBsRkQcHxHT8vv5wLKImAwsy++RdAxpmvljSSslXiFpVCcCm5mNVHUrIAPNAq7Jr68Bzmxo74uIHRGxHlgHnNj+eGZmI1edCkgA35e0UtLc3NYTEZsB8nP/lPHjgYcajt2Y28zMrE0UEZ3OAICkIyLiYUmHA0uBd5FWPjykYZ9fR8Shkr4A3BkRX83ti4BbIuJbTT53LjAXoKenZ2pfX1+pfKs2PTak/XtGw5anSn1VWzlntbohZ5UZp4w/uJoPamL79u2MGTOmZZ9flW7IOdyMM2bMWNkwtPAHhddEb7WIeDg/b5V0I6lLaoukcRGxWdI4YGvefSMwseHwCcDDu/nchcBCgGnTpkVvb2+pfHOGuGrbvCk7uXRVbf54d8s5q9UNOavMuOGc3ko+p5nly5dT9u9rO3VDzlZlrEUXlqQDJT2r/zXwSmA1sAQ4N+92LnBTfr0EmC1pP0lHkVZPvLu9qc3MRra6/FOpB7gxL5m7D/C1iPiupJ8AiyW9FXgQeD1ARKyRtBi4D9gJnB8RuzoT3cxsZKpFAYmIXwAvbtL+S+CU3RxzMXBxi6OZmdlu1KILy8zMuo8LiJmZleICYmZmpdRiDMTMutOkIV7e3mjDgtMrTGKd4DMQMzMrxQXEzMxKcQExM7NSXEDMzKwUFxAzMyvFBcTMzEpxATEzs1JcQMzMrBQXEDMzK8UFxMzMSnEBMTOzUlxAzMysFBcQMzMrxQXEzMxKcQExM7NSXEDMzKwUFxAzMyvFKxKaWUfsaTXDeVN2Mmc3+3g1w3rwGYiZmZXiAmJmZqW4C8vMus6eur8G4+6v6vgMxMzMSnEBMTOzUlxAzMysFBcQMzMrxQXEzMxK8VVYZjaiDOcKLvBVXI18BmJmZqW4gJiZWSkuIGZmVkpXj4FImgl8FhgFfDkiFnQ4kpnt5QaOoQw26eNAwxk/Gc7YzdUzDyx97GC69gxE0ijgC8CrgWOAsyUd09lUZmYjRzefgZwIrIuIXwBI6gNmAfd1NJWZ2W4M9wqwulFEdDpDKZJeB8yMiL/N798MvCwi3jlgv7nA3Pz2+cD9bYo4Fni0Td81HM5ZrW7I2Q0ZwTmrNNyMfx4RzxnY2M1nIGrS9oxqGBELgYWtj/NfSVoREdPa/b1D5ZzV6oac3ZARnLNKrcrYtWMgwEZgYsP7CcDDHcpiZjbidHMB+QkwWdJRkv4UmA0s6XAmM7MRo2u7sCJip6R3At8jXcZ7VUSs6XCsRm3vNivJOavVDTm7ISM4Z5VakrFrB9HNzKyzurkLy8zMOsgFxMzMSnEBqYCkiZJul7RW0hpJ787th0laKumB/HxoBzPuL+luST/NGT9at4yNJI2S9G+Sbs7va5dT0gZJqyTdK2lFjXMeIumbkn6Wf0f/ok45JT0//xn2P7ZJuqBOGRuyvif//Vkt6fr896qOOd+dM66RdEFuqzynC0g1dgLzIuKFwHTg/DytynxgWURMBpbl952yAzg5Il4MHA/MlDSdemVs9G5gbcP7uuacERHHN1xjX8ecnwW+GxEvAF5M+nOtTc6IuD//GR4PTAWeBG6sU0YASeOBfwCmRcRxpIt3ZlO/nMcBbyPN1vFi4AxJk2lFzojwo+IHcBPwP0h3vY/LbeOA+zudLWc5ALgHeFkdM5Lu6VkGnAzcnNvqmHMDMHZAW61yAgcB68kXzNQ1Z0OuVwI/qmNGYDzwEHAY6QrWm3PeuuV8PWly2f73HwL+dyty+gykYpImAS8Bfgz0RMRmgPx8eAej9XcL3QtsBZZGRO0yZp8h/cI/3dBWx5wBfF/SyjxlDtQv53OB/wT+b+4S/LKkA6lfzn6zgevz61pljIhNwKeAB4HNwGMR8X1qlhNYDZwk6dmSDgBOI910XXlOF5AKSRoDfAu4ICK2dTrPQBGxK1I3wQTgxHyqWyuSzgC2RsTKTmcp4OURcQJpRujzJZ3U6UBN7AOcAFwZES8BnqAe3WrPkG8Ifg3wjU5naSaPGcwCjgKOAA6U9KbOpnqmiFgLfAJYCnwX+Cmpm71yLiAVkbQvqXhcFxE35OYtksbl7eNI//LvuIj4DbAcmEn9Mr4ceI2kDUAfcLKkr1K/nETEw/l5K6nP/kTql3MjsDGfbQJ8k1RQ6pYTUiG+JyK25Pd1y3gqsD4i/jMifg/cAPw36peTiFgUESdExEnAr4AHaEFOF5AKSBKwCFgbEZc1bFoCnJtfn0saG+kISc+RdEh+PZr0l+Fn1CgjQERcGBETImISqTvjtoh4EzXLKelASc/qf03qC19NzXJGxCPAQ5Ken5tOIS15UKuc2dn8sfsK6pfxQWC6pAPy3/lTSBck1C0nkg7Pz0cCZ5H+XKvP2cnBnr3lAfwlqT/834F78+M04NmkweAH8vNhHcz4IuDfcsbVwEW5vTYZm2Tu5Y+D6LXKSRpb+Gl+rAE+WMecOdPxwIr83/7bwKF1y0m6sOOXwMENbbXKmDN9lPQPr9XAV4D9aprzX0n/UPgpcEqr/jw9lYmZmZXiLiwzMyvFBcTMzEpxATEzs1JcQMzMrBQXEDMzK8UFxKxFlKyXFJKe1+k8ZlVzATFrnb8AJuXXszuYw6wlXEDMWuds0txTP86vzfYqLiBmLSBpFGla7SXAVcAxkl40YJ9eSf8u6beSfiLpREmPSvrIgP1mSVqR93tE0ifz3GtmHeUCYtYaJwM9pAkhvwn8noazkLw40S2kCe1eB/wTcB0wuvFDJL2BNGnf3aSZaj8KzAUuaflPYLYH+3Q6gNle6mzgN6SVAH8naSkwW9IHIs0fdAFp5b2/ioinACRtA77e/wF5wr7/A1wbEe9oaN8BfEHSJRHxy3b9QGYD+QzErGKS9gNeC9wYEb/LzdeTBtSn5/cvJS3q9VTDoUsGfNTRwJHAYkn79D+A24D9gdqt52IjiwuIWfVeDRwC3CLpkDyN/nLSuvT93Vh/Rlop8A8i4rfA9oamsfn5FlIXWP9jfW6fWH10s+LchWVWvf4i0WxlvTdIeg/wCPCcxg2S9gfGNDT9Kj/PJU3FP9D6Jm1mbeMCYlahvKzxGaQuq4UDNr8EuAyYAfwE+BtJoxu6sV4zYP/7gU3ApIj4UutSm5XjAmJWrVmkxZE+G39cRhYAST8CPkg6Q7kIOB/4Z0mfJnVpzScNrD8NEBFPS5oHfEXSQcCtwO9Ii1mdCbwuIp5sxw9l1ozHQMyqdTbwwMDiARBpHe3FpCVGHwVOBw4nXab7LuA8YBSwreGYr5OK0vGkLrEbgHcA95CKiVnHeEVCs5qQ9JekpUhPjojbO53HbE9cQMw6RNInSIPjjwDPBz5EWhf8JRHxdCezmRXhMRCzztmPdKNgD/A48H3gvS4e1i18BmJmZqV4EN3MzEpxATEzs1JcQMzMrBQXEDMzK8UFxMzMSvn/aWJxq4EFJBYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "ml_age=ml['age']\n",
    "ml_age.hist(density=False, histtype='stepfilled', bins=20)\n",
    "\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Male samples',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age=fm['age']\n",
    "\n",
    "fm_age.hist(density=False, histtype='stepfilled', bins=10)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Female samples',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare both populations: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "fm_age.hist(density=False, histtype='stepfilled', alpha=.5, bins=20)   # default number of bins = 10\n",
    "ml_age.hist(density=False, histtype='stepfilled', alpha=.5, color=sns.desaturate(\"indianred\", .75), bins=10)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Samples',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age.hist(density=True, histtype='stepfilled', alpha=.5, bins=20)   # default number of bins = 10\n",
    "ml_age.hist(density=True, histtype='stepfilled', alpha=.5, color=sns.desaturate(\"indianred\", .75), bins=10)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('PMF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 Data Distributions\n",
    "\n",
    "Summarizing can be dangerous: very different data can be described by the same statistics. It must be validated by inspecting the data.\n",
    "\n",
    "We can look at the **data distribution**, which describes how often (frequency) each value appears.\n",
    "\n",
    "\n",
    "We can normalize the frequencies of the histogram by dividing/normalizing by $n$, the number of samples. The normalized histogram is called **Probability Mass Function (PMF)**.\n",
    "\n",
    "Let's visualize and compare the MPF of male and female age in our example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAELCAYAAAAcKWtPAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAeC0lEQVR4nO3df5gdVZ3n8ffHAEMggxHBnkyIJIzRNUvWEHpCkFmnA+KTABpZQZPhN2LkkaygcZforqvIOEZmkJUdJjFIFhiRGBWHLLSDMdLr4AyShEGSELJEyAMJIQhCoPlpy3f/qNOTy81N97237q2+l/68nuc+XXXqnKpv3aTzTZ1TdUoRgZmZWR5vGuoAzMys/TmZmJlZbk4mZmaWm5OJmZnl5mRiZma57TPUAQyVQw45JMaPH1/Y8V544QUOPPDAwo5Xj3aIERxnI7VDjOA4Gy1PnOvWrXsqIg7dY0NEDMvP0UcfHUW68847Cz1ePdohxgjH2UjtEGOE42y0PHECa6PCv6nu5jIzs9ycTMzMLDcnEzMzy83JxMzMcnMyMTOz3JxMzMwsNycTMzPLzcnEzMxyczIxM7Pchu10Klab8Qtvr7vt1kUnNzASM2tFvjIxM7PcCk8mkmZK2ixpi6SFFbZL0tVp+/2Spqby/SXdI+lXkjZKuqykzcGSVkl6KP18S5HnZGY23BWaTCSNAK4BZgGTgLmSJpVVmwVMTJ95wOJU/gpwfES8B5gCzJQ0PW1bCKyOiInA6rRuZmYFKfrKZBqwJSIejohXgeXA7LI6s4Eb0wSVdwOjJY1J672pzr7pEyVtbkjLNwAfbuZJmJnZ6ymbUbigg0mnATMj4oK0fhZwTETML6lzG7AoIu5K66uBSyNibbqyWQe8A7gmIi5NdZ6NiNEl+3gmIvbo6pI0j+xqh46OjqOXL1/epDPdU29vL6NGjSrsePUYKMb123fVvd/JY99cd9tK2uG7hPaIsx1iBMfZaHninDFjxrqI6CwvL/puLlUoK89me60TEb8HpkgaDfxI0pERsaHag0fEUmApQGdnZ3R1dVXbNLeenh6KPF49Borx3Dx3c51ReZ/1aofvEtojznaIERxnozUjzqK7ubYB40rWDwMer7VORDwL9AAzU9FOSWMA0s8nGxaxmZkNquhksgaYKGmCpP2AOcDKsjorgbPTXV3TgV0RsUPSoemKBEkjgfcDD5a0OSctnwPc2uTzMDOzEoV2c0VEn6T5wB3ACGBZRGyUdGHavgToBk4CtgAvAuel5mOAG9K4yZuAFRFxW9q2CFgh6ePAo8DpRZ2TmZkNwRPwEdFNljBKy5aULAdwUYV29wNH7WWfTwMnNDZSMzOrlp+ANzOz3JxMzMwsN0/0OIwMNlnjgsl9uW4BNrPhy1cmZmaWm5OJmZnl5mRiZma5OZmYmVluTiZmZpab7+ayllbpDrRa7jrzK4PNiuErEzMzy83JxMzMcnMyMTOz3JxMzMwsNycTMzPLzcnEzMxyczIxM7PcnEzMzCw3JxMzM8vNycTMzHJzMjEzs9w8N5e9oQ32dsmBeF4vs+r5ysTMzHJzMjEzs9ycTMzMLDcnEzMzy63wZCJppqTNkrZIWlhhuyRdnbbfL2lqKh8n6U5JmyRtlHRxSZsvS9ou6b70OanIczIzG+4KvZtL0gjgGuBEYBuwRtLKiHigpNosYGL6HAMsTj/7gAURca+kPwTWSVpV0vaqiPibos7FzMx2K/rKZBqwJSIejohXgeXA7LI6s4EbI3M3MFrSmIjYERH3AkTE88AmYGyRwZuZWWWKiOIOJp0GzIyIC9L6WcAxETG/pM5twKKIuCutrwYujYi1JXXGAz8HjoyI5yR9GTgXeA5YS3YF80yF488D5gF0dHQcvXz58macZkW9vb2MGjWqsONVsn77rgG3d4yEnS81/riTx7657raVYm5WnOXyxA2t8Wc+mHaIERxno+WJc8aMGesiorO8vOiHFlWhrDybDVhH0ijgh8AlEfFcKl4MXJ7qXQ5cCZy/x04ilgJLATo7O6Orq6vG8OvX09NDkcer5NxBHuBbMLmPK9c3/q/E1jO66m5bKeZmxVkuT9zQGn/mg2mHGMFxNloz4iy6m2sbMK5k/TDg8WrrSNqXLJHcFBG39FeIiJ0R8fuIeA24lqw7zczMClJ0MlkDTJQ0QdJ+wBxgZVmdlcDZ6a6u6cCuiNghScB1wKaI+EZpA0ljSlZPBTY07xTMzKxcod1cEdEnaT5wBzACWBYRGyVdmLYvAbqBk4AtwIvAean5ccBZwHpJ96WyL0REN3CFpClk3VxbgU8WckJmZgYMwUSP6R//7rKyJSXLAVxUod1dVB5PISLOanCYZmZWAz8Bb2ZmuTmZmJlZbk4mZmaWm5OJmZnl5mRiZma5OZmYmVluTiZmZpZb4c+Z2PAzfpA5wcys/TmZFCzvP6xbF53coEjMzBrH3VxmZpabk4mZmeXmZGJmZrk5mZiZWW5OJmZmlpuTiZmZ5eZkYmZmuTmZmJlZbjUlE0mnSHICMjOz16k1MdwKbJf0dUnvbkZAZmbWfmpNJn8CLAU+CmyQ9C+SPiHpoMaHZmZm7aKmZBIRWyPiSxExATgR2AJcBeyQ9PeSZjQjSDMza211j39ExM8i4izgncA64Azgp5IekfQZSZ5E0sxsmKg7mUj6c0nXA5uBI4FrgA8A3wcuA25sRIBmZtb6arp6kHQ4cE76jAd6gHnALRHxSqq2WtK/AN9pXJhmZtbKar0yeRj4BPBd4B0RcUJE3FySSPptBO6ptANJMyVtlrRF0sIK2yXp6rT9fklTU/k4SXdK2iRpo6SLS9ocLGmVpIfSz7fUeF5mZpZDrcnkg8DhEfHFiHhkb5Ui4v9FxB6D8ZJGkHWHzQImAXMlTSqrNguYmD7zgMWpvA9YEBHvBqYDF5W0XQisjoiJwOq0bmZmBak1mZwGHF5pg6TDJS0bpP00YEtEPBwRrwLLgdlldWYDN0bmbmC0pDERsSMi7gWIiOeBTcDYkjY3pOUbgA/XeF5mZpaDIqL6ytLvgWMjYo8uLElHA/dExIgB2p8GzIyIC9L6WcAxETG/pM5twKKIuCutrwYujYi1JXXGAz8HjoyI5yQ9GxGjS7Y/ExF7dHVJmkd2tUNHR8fRy5cvr/rc8+rt7WXUqFGs374r134mj31z3W0HO3bHSNj5Ut27L0xRceb5rmH3n3kra4cYwXE2Wp44Z8yYsS4iOsvLa719V8Dess+RwG+qaF+ufH8D1pE0CvghcElEPDfI8V6/k4ilZA9d0tnZGV1dXbU0z6Wnp4euri7OzfsO+DO66m472LEXTO7jyvWtf0d3UXHm+a5h9595K2uHGMFxNloz4hz0NzINdPcPdgfwD5LKB9z3BzqA6wfZ3TZgXMn6YcDj1daRtC9ZIrkpIm4pqbOzvytM0hjgyUHiMDOzBqrmv3cPkP0DLuCzwJ3AjrI6rwIPAisG2dcaYKKkCcB2YA7wF2V1VgLzJS0HjgF2pSQh4DpgU0R8o0Kbc4BF6eetVZxXWxqf88rGzKwZBk0mEbEKWAUg6Xng2xGxvZ6DRUSfpPnAHcAIYFlEbJR0Ydq+BOgGTiKbquVF4LzU/DjgLGC9pPtS2RciopssiayQ9HHgUeD0euIza5TxC29nweS+uro1ty46uQkRmTVXTR3PEXFZ3gOmf/y7y8qWlCwHcFGFdndReTyFiHgaOCFvbGZmVp9qxkxWAJ+PiF+n5YFERHysMaGZmVm7qObK5FBg37T8NvZ+N5eZmQ1T1YyZzChZ7mpqNGZm1pb8Cl4zM8utmjGTT9Wyw4j4u/rDMTOzdlTNmMnf1rC/AJxMzMyGmWrGTNwVZmZmA3KiMDOz3KoZM5kE/DoiXqnw7pE9RMQDDYnMzMzaRjVjJhvIXkZ1T1re23Mm/TMK73UKejMze2OqJpnMIJvssX/ZzMzsdaoZgP+/lZbNzMz61fWGIUnvAv4UGEM2Hf3aiHiwkYGZmVn7qCmZSDoIuBb4CNmdYL3AKOA1SbcAF9T69kMzM2t/td4a/HfAB4CzgQMi4iDgALIXUp2IH1g0MxuWau3mmg18JiK+218QES8DN0k6ACh/A6KZmQ0DtV6Z9LLnK3v7PQ68kC8cMzNrR7Umk2uAz0kaWVqYrko+h7u5zMyGpWqegL+irGgi8JikVcCTZC/MOhF4CVjb8AjNzKzlVTNmcnrZ+u/SZ3pJ2fPp50eA/9KAuMzMrI1U89DihCICMTOz9lXXQ4tmw8H4hbcPdQhmbaPmZCJJwHHAO4H9y7f7TYtmZsNPrU/AdwCrgUlkMwQrbSqdSdjJxMxsmKn1yuRKYBcwDngMOAbYCZxJ9lT8yQ2NrkXV0/2xYHIf57rbxMzeoGp9zuTPyRJK/4OLiohHI+KvgO9QxVWJpJmSNkvaImlhhe2SdHXafr+kqSXblkl6UtKGsjZflrRd0n3pc1KN52VmZjnUmkxGA7+JiNeA58ieMen3z8B7B2osaQTZg4+zyLrK5lZ4e+MssmdZJgLzgMUl264HZu5l91dFxJT06a7qbMzMrCFqTSaPkE07D7AROKNk2weB3w7SfhqwJSIejohXgeVk832Vmg3cGJm7gdGSxgBExM+rOIaZmRWs1jGT28lmDV4B/CVwq6RtZA8xvh24dJD2Y8nGWvptIxt3GazOWPY+J1i/+ZLOJnsKf0FEPFNeQdI8sqsdOjo66OnpGWSXlS2Y3Fdzm46R9bUrUjvECG/8OOv9e1mP3t7eQo9XL8fZWM2Is6ZkEhGfL1n+saTjgFPJbhFeFRE/HmQXqlBW/k75auqUWwxcnupdTjauc/4eO4lYCiwF6OzsjK6urkF2W1k9A+kLJvdx5frWfqynHWKEN36cW8/oanwwe9HT00O9vwdFcpyN1Yw4c/1GRsQaYE0NTbaR3QnW7zCy2YZrrVMex87+ZUnXArfVEJOZmeVU72t7P0A2/tH/2t5fRsSqKpquASZKmgBsB+YAf1FWZyVZl9Vysi6wXRExYBeXpDEldU4FNgxU38zMGqvWhxb/GPgR2fvfn2T3rMFfkbQWODUitu+tfUT0SZoP3AGMAJZFxEZJF6btS4Bu4CRgC/AicF7J8W8GuoBD0ljNlyLiOuAKSVPIurm2Ap+s5bzMzCyfWq9MlpJdjfxZRPxzf2EaO7kZ+BZwykA7SLftdpeVLSlZDuCivbSdu5fys6qM38zMmqDWZHI8cH5pIgGIiF+kBxCvbVhkZsNU3gkmty4aFhNRWIup9TmTnWQvwarkJeCpfOGYmVk7qjWZ/BXZ+MhhpYVp/UvAVxsVmJmZtY9qXtu7oqzorcCvJd3L7gH4qWn5/aTnOMzMbPioZszk0LL1h9IH4CDgZbJ5uQAOaVBcZmbWRqp5be+MIgIxM7P2VeuYyetI2rdRgZiZWfuqOZlIeq+kH0t6HnhZ0vOSuiUd24T4zMysDdT6BPyJZDMHbwb+muxW4Q7gNKBH0skR8dOGR2lmZi2t1ocWv0o2d9bp6Un1fl+R9EOyW4edTMzMhplau7kmA9eWJZJ+S9N2MzMbZmpNJs8Cf7KXbe9I283MbJipNZl8H/iapDMl7Q8gaX9JZ5J1gZU/4GhmZsNArWMml5I9AX8DcIOkXmBU2nYzg7+218zM3oBqfW3vS8AZki4ne6dJ/8ux1kTEg02Iz8zM2kDVySR1a+0CPhYR/wA4eZiZGVDDmElEvEw2mWNf88IxM7N2VOsA/LeAT3saFTMzK1XrAPxo4Ehgq6TVZE/Alz5zEhHhQXgzs2Gm1mTyEeCVtPwfK2wPfEeXmdmwU1UykTQSOAn4W+AJ4KcRsbOZgZmZWfuo5k2LR5DNtzW+pHiXpI9FxE+aFZiZmbWPagbgrwBeI+vWOgD498B9ZIPxZmZmVSWTY4H/HhG/iIiXI2IT8Eng7ZLGNDc8MzNrB9UkkzHAw2VlvwYE/FGtB5Q0U9JmSVskLaywXZKuTtvvlzS1ZNsySU9K2lDW5mBJqyQ9lH6+pda4zMysftU+Z1JpyvmaSRoBXAPMAiYBcyVNKqs2C5iYPvOAxSXbrgdmVtj1QmB1REwEVqd1MzMrSLW3Bt8hqdKT76vLyyPibQPsZxqwJSIeBpC0HJgNPFBSZzZwY3pnyt2SRksaExE7IuLnksZX2O9soCst3wD04FuUzcwKU00yuayBxxsLPFayvg04poo6Y8kmlNybjojYARAROyQNlNDMzKzBBk0mEdHIZKJKh6ijTn0Hl+aRdZ3R0dFBT09PXftZMLn26ck6RtbXrkjtECM4zsHU8ve6t7e37t+DIjnOxmpGnLU+AZ/XNmBcyfphwON11Cm3s78rLN1h9mSlShGxlOz1wnR2dkZXV1cNoe927sLba26zYHIfV64v+uuuTTvECI5zMFvP6Kq6bk9PD/X+HhTJcTZWM+KsdaLHvNYAEyVNkLQfMAdYWVZnJXB2uqtrOrCrvwtrACuBc9LyOcCtjQzazMwGVuh/myKiT9J84A5gBLAsIjZKujBtXwJ0k03dsgV4ETivv72km8kG2g+RtA34UkRcBywCVkj6OPAocHpxZ2XWWsbXcOW8YHLf6660ty46uRkh2TBQ+DV4RHSTJYzSsiUlywFctJe2c/dS/jRwQgPDNDOzGhTdzWVmZm9ATiZmZpabk4mZmeXW+vdXmllhahm8L+fB++HNVyZmZpabk4mZmeXmZGJmZrk5mZiZWW5OJmZmlpuTiZmZ5eZkYmZmuTmZmJlZbk4mZmaWm5OJmZnl5mRiZma5OZmYmVluTiZmZpabk4mZmeXmZGJmZrk5mZiZWW5OJmZmlpuTiZmZ5eZkYmZmuTmZmJlZbk4mZmaWW+HJRNJMSZslbZG0sMJ2Sbo6bb9f0tTB2kr6sqTtku5Ln5OKOh8zMys4mUgaAVwDzAImAXMlTSqrNguYmD7zgMVVtr0qIqakT3dzz8TMzEoVfWUyDdgSEQ9HxKvAcmB2WZ3ZwI2RuRsYLWlMlW3NzGwI7FPw8cYCj5WsbwOOqaLO2Crazpd0NrAWWBARz5QfXNI8sqsdOjo66OnpqeskFkzuq7lNx8j62hWpHWIEx9lIjYzxf910a91tJ49984Dbe3t76/59LdJwjrPoZKIKZVFlnYHaLgYuT+uXA1cC5+9ROWIpsBSgs7Mzurq6qgq63LkLb6+5zYLJfVy5vuivuzbtECM4zkZqlRi3ntE14Paenh7q/X0t0nCOs+i/RduAcSXrhwGPV1lnv721jYid/YWSrgVua1zIZmY2mKLHTNYAEyVNkLQfMAdYWVZnJXB2uqtrOrArInYM1DaNqfQ7FdjQ7BMxM7PdCr0yiYg+SfOBO4ARwLKI2CjpwrR9CdANnARsAV4Ezhuobdr1FZKmkHVzbQU+WdhJmZlZ4d1cpNt2u8vKlpQsB3BRtW1T+VkNDtPMzGrgJ+DNzCw3JxMzM8vNycTMzHJzMjEzs9ycTMzMLDcnEzMzy83JxMzMcnMyMTOz3JxMzMwsNycTMzPLzcnEzMxyczIxM7Pchv6tOGY27I0f5IVzCyb37fWldFsXndyMkKxGvjIxM7PcnEzMzCw3d3OZWVsbrItsMO4mawxfmZiZWW5OJmZmlpuTiZmZ5eZkYmZmuTmZmJlZbr6by8yGtTx3g/lOsN18ZWJmZrk5mZiZWW5OJmZmllvhYyaSZgLfBEYA346IRWXblbafBLwInBsR9w7UVtLBwPeA8cBW4KMR8UwR52Nmw1f5eMtAE1KWyzPekvep/+tnHpirfSWFXplIGgFcA8wCJgFzJU0qqzYLmJg+84DFVbRdCKyOiInA6rRuZmYFKfrKZBqwJSIeBpC0HJgNPFBSZzZwY0QEcLek0ZLGkF117K3tbKArtb8B6AEubfbJmJnVK+/VRaspOpmMBR4rWd8GHFNFnbGDtO2IiB0AEbFD0tsqHVzSPLKrHYBeSZvrOYl6fBoOAZ4q6nj1aIcYwXE2UjvECI6z0WZ8PVech1cqLDqZqEJZVFmnmrYDioilwNJa2jSKpLUR0TkUx65WO8QIjrOR2iFGcJyN1ow4i76baxswrmT9MODxKusM1HZn6goj/XyygTGbmdkgik4ma4CJkiZI2g+YA6wsq7MSOFuZ6cCu1IU1UNuVwDlp+Rzg1mafiJmZ7VZoN1dE9EmaD9xBdnvvsojYKOnCtH0J0E12W/AWsluDzxuobdr1ImCFpI8DjwKnF3ha1RqS7rUatUOM4DgbqR1iBMfZaA2PU9lNU2ZmZvXzE/BmZpabk4mZmeXmZNJgksZJulPSJkkbJV2cyg+WtErSQ+nnW4Y4zv0l3SPpVynOy1oxzhTTCEn/Kum2Fo5xq6T1ku6TtLaF4xwt6QeSHkx/R49ttTglvSt9j/2f5yRd0oJxfib97myQdHP6nWqpGFOcF6cYN0q6JJU1PE4nk8brAxZExLuB6cBFadqXVpvy5RXg+Ih4DzAFmJnunmu1OAEuBjaVrLdijAAzImJKyf37rRjnN4F/jIh/B7yH7HttqTgjYnP6HqcAR5PdiPMjWihOSWOBTwOdEXEk2U1Bc1opRgBJRwKfIJt95D3AKZIm0ow4I8KfJn7IblM+EdgMjEllY4DNQx1bSYwHAPeSzSjQUnGSPU+0GjgeuC2VtVSMKY6twCFlZS0VJ3AQ8AjpxptWjbMstg8Av2i1ONk9I8fBZHfF3pZibZkYUwynk02K27/+ReC/NiNOX5k0kaTxwFHALymb8gWoOOVLkVL30X1kD3muiohWjPN/kv3lf62krNVihGw2hp9IWpem7YHWi/MI4DfA/07dht+WdCCtF2epOcDNabll4oyI7cDfkD2KsIPsebiftFKMyQbgfZLeKukAsscuxtGEOJ1MmkTSKOCHwCUR8dxQx1NJRPw+sq6Ew4Bp6ZK4ZUg6BXgyItYNdSxVOC4ippLNan2RpPcNdUAV7ANMBRZHxFHAC7RG11tF6eHkDwHfH+pYyqUxhtnABOCPgQMlnTm0Ue0pIjYBXwdWAf8I/IqsK77hnEyaQNK+ZInkpoi4JRW37JQvEfEs2UzLM2mtOI8DPiRpK7AcOF7Sd2itGAGIiMfTzyfJ+ven0XpxbgO2pStQgB+QJZdWi7PfLODeiNiZ1lspzvcDj0TEbyLid8AtwHtbLEYAIuK6iJgaEe8Dfgs8RBPidDJpMEkCrgM2RcQ3Sja11JQvkg6VNDotjyT75XiQFoozIj4fEYdFxHiy7o6fRcSZtFCMAJIOlPSH/ctkfecbaLE4I+IJ4DFJ70pFJ5C9wqGl4iwxl91dXNBacT4KTJd0QPqdP4HsZoZWihEApVnUJb0d+E9k32nD4/QT8A0m6c+AfwLWs7uf/wtk4yYrgLeTpnyJiN8OSZCApP9A9u6XEWT/qVgREV+R9NZWirOfpC7gcxFxSqvFKOkIsqsRyLqSvhsRX221OAEkTQG+DewHPEw2XdGbaL04DyAb4D4iInalspb6PpXdTv8xsm6jfwUuAEa1UowAkv4JeCvwO+CzEbG6Gd+lk4mZmeXmbi4zM8vNycTMzHJzMjEzs9ycTMzMLDcnEzMzy83JxKwAyjwiKSS9Y6jjMWs0JxOzYhwLjE/Lc4YwDrOmcDIxK8ZcsrmwfpmWzd5QnEzMmkzSCLKpwFcCy4BJaQaC0jpdku6X9LKkNZKmSXpK0pfL6s2WtDbVe0LSFWkuOLMh5WRi1nzHAx1kk1X+gGxai3+7OkkvWuomm2zvNOBbwE3AyNKdSPoo2YSC95DNpnsZMA/4WtPPwGwQ+wx1AGbDwFzgWbI3HL4qaRUwR9IXIpvP6BKytwl+MCJeApD0HPC9/h2kyQT/GrgxIj5VUv4KcI2kr0XE00WdkFk5X5mYNZGkPwBOBX4UEa+m4pvJBuOnp/U/JXs52UslTVeW7eqdZJPyrZC0T/8H+BmwP9BS76Kx4cfJxKy5ZgGjgW5Jo9O0/z3AK+zu6vojsjcg/puIeBnoLSk6JP3sJusm6/88ksrHNT50s+q5m8usufoTRqW3BX5U0meAJ4BDSzdI2p9sOvN+/dODzyOb7rzcIxXKzArjZGLWJOnVzaeQdWstLdt8FPANYAawBjhP0siSrq4PldXfDGwHxkfEtc2L2qw+TiZmzTMbOAD4ZsmrcgGQ9Avgv5FdufwP4CLg/0i6iqzbayHZoPxrABHxmqQFwN9LOgj4MfAqcATwYeC0iHixiJMyq8RjJmbNMxd4qDyRAKT3hq8ge43qU8DJwNvIbv39z8D5ZG/BfK6kzffIEtQUsm6zW4BPAfeSJRazIeM3LZq1oJLXPx8fEXcOdTxmg3EyMWsBkr5ONrD+BPAu4IvA08BREfHaUMZmVg2PmZi1hj8geyixA3ge+AnwWScSaxe+MjEzs9w8AG9mZrk5mZiZWW5OJmZmlpuTiZmZ5eZkYmZmuf1/0MuoJt/pBSwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(density=True, histtype='stepfilled', bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Probability',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age.hist(density=True, histtype='stepfilled', bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Probability',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **cumulative distribution function (CDF)**, or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found to have a value less than or equal to x. For our example, the CDFs will be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(density=True, histtype='step', cumulative=True, linewidth=3.5, bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age.hist(density=True, histtype='step', cumulative=True, linewidth=3.5, bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(bins=10, density=True, histtype='stepfilled', alpha=.5)   # default number of bins = 10\n",
    "fm_age.hist(bins=10, density=True, histtype='stepfilled', alpha=.5, color=sns.desaturate(\"indianred\", .75))\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Probability',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(density=True, histtype='step', cumulative=True,  linewidth=3.5, bins=20)\n",
    "fm_age.hist(density=True, histtype='step', cumulative=True,  linewidth=3.5, bins=20, color=sns.desaturate(\"indianred\", .75))\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean sample difference is  2.5753170652810553\n"
     ]
    }
   ],
   "source": [
    "print(\"The mean sample difference is \", ml_age.mean() - fm_age.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 Outliers\n",
    "\n",
    "**Ouliers** are data samples with a value that is far from the central tendency.\n",
    "\n",
    "We can find outliers by:\n",
    "\n",
    "+ Computing samples that are *far* from the median.\n",
    "+ Computing samples whose value *exceeds the mean* by 2 or 3 standard deviations.\n",
    "\n",
    "This expression will return a series of boolean values that you can then index the series by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['age'].median()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how many outliers we can detect in our example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df[(df.income == '>50K\\n') & (df['age'] < df['age'].median() - 15)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df[(df.income == '>50K\\n') & (df['age'] > df['age'].median() + 35)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we think that outliers correspond to errors, an option is to trim the data by discarting the highest and lowest values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32492, 15)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = df.drop(df.index[(df.income=='>50K\\n') & (df['age']>df['age'].median() + 35) & (df['age'] > df['age'].median() -15)])\n",
    "df2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml1_age=ml1['age']\n",
    "fm1_age=fm1['age']\n",
    "\n",
    "ml2_age = ml1_age.drop(ml1_age.index[(ml1_age > df['age'].median() + 35) & (ml1_age > df['age'].median() - 15)])\n",
    "fm2_age = fm1_age.drop(fm1_age.index[(fm1_age > df['age'].median() + 35) & (fm1_age > df['age'].median() - 15)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Men statistics: Mean: 44.317982123920615 Std: 10.019749857171412 Median: 44.0 Min: 19 Max: 72\n"
     ]
    }
   ],
   "source": [
    "mu2ml = ml2_age.mean()\n",
    "std2ml = ml2_age.std()\n",
    "md2ml = ml2_age.median()\n",
    "# Computing the mean, std, median, min and max for the high-income male population\n",
    "print(\"Men statistics: Mean:\", mu2ml, \"Std:\", std2ml, \"Median:\", md2ml, \"Min:\", ml2_age.min(), \"Max:\", ml2_age.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Women statistics: Mean: 44.317982123920615 Std: 10.019749857171412 Median: 44.0 Min: 19 Max: 72\n"
     ]
    }
   ],
   "source": [
    "mu3ml = fm2_age.mean()\n",
    "std3ml = fm2_age.std()\n",
    "md3ml = fm2_age.median()\n",
    "# Computing the mean, std, median, min and max for the high-income female population\n",
    "print(\"Women statistics: Mean:\", mu2ml, \"Std:\", std2ml, \"Median:\", md2ml, \"Min:\", fm2_age.min(), \"Max:\", fm2_age.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean difference with outliers is: 2.58.\n",
      "The mean difference without outliers is: 2.44.\n"
     ]
    }
   ],
   "source": [
    "print('The mean difference with outliers is: %4.2f.' % (ml_age.mean() - fm_age.mean()))\n",
    "print(\"The mean difference without outliers is: %4.2f.\" % (ml2_age.mean() - fm2_age.mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare visually the age distributions before and after removing the outliers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Samples')"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lAC7OUBpynoze5d1a4nIAWyCymwTPaT24ezKL+9s9Yls2MrYtmz9jlqH73UTCeJPMqDwtlGSqsnEFgIcjf0+TUrYAQOR3XYbSQCpGO/ux+46nEBzWP/VtWtdLFt+psz2f2PfY2+hauRmAzsMgJarfeR6+Ln1Phvc+tALd7zWmkcLco3c/6zHWM4Rdv3lyYtxLtp+PiYr3NqJy3QrTn297cS3aXrRxuuCEHd784GvYvzazTxZDY+PY/btnJvrwDzV3Y/fvn0UoEMxoOtzC17IHVe+/kjTuqfu9RjQuuX0iv8sVVt0+o/srNlBLz7pdaF663JoN6DTS3oeGx25HYUdzRrebKT3rdqFxye3Yv2aH00lxlO2VDSFEAYDPAXjc4OduEEKsFkKs7siXqVAd0v7USgS27sD+d7c6nRTXy+J6EgBgaMW72P/Q87qXF/19KNmzGZVvPqtr+eGVa9D9Z+N961W3H7kRChjb8dlQCDeTxo7n38N44050rthofYJcoGblMyjban6ukP5/vI7+f7ye9Lq06entyKoP0HXvk7asG1A+R/o+2oPA5ka0PRIO79r+l5cR+HgbBhpb099gFmZw1a8+htKdG5LSHs2HjOR3Sly1SyzM2KJ5qoxZZ+fdf8fIu+ss24YeLfeHwwbXvv5oRrebKZ13h0P8d933lMMpcVYmWjbOB7BWShl9NNomhKgHgMjvdqUPSSnvllIuklIuqq2tzUAyidzDLTc4x9ORDbUGJ3C/EMVzMmKdy65HPfm2eyLguSUdmeX4vTXDMlHZuBKTXagA4FkAiyN/LwZg3WNQyhvBkQCGmrudToZjjNzbgiOBlOEsxdgoAp36gg+MtPcZDl+btjRz5oGdHUk31+BIAMMtPWmtV81IWy/GB0etX3FkP7isbJPzxofGdF8fiUKBoKV5lV2FlED/CIK94YAFY63dmt2yxnqGMhKCXQZDGNytbzC+E4VnkYES48DOjrQOemhsXPn8i6xTtmVnz5HBpi7Luw4Ot/RgfEh/d/LxwdGsCDvrBrZWNoQQJQDOBhDbznwbgLOFENsi791mZxpIv0wNfrMif27+03PY98sH8rafshF7/vdJ7P3F/ZrLTHv1IUx//l71BWJKt8233oPdP/uzRanTZsXEjwONrWj99YNoffa9uNeb7vg79v7HfWmvX0nzz+5F0y8eTLmcZK0hKzT96mHt60ND8/2vYN8vH0hrfiVl1p47TT+5B8GmcFS0oddXYe+fl6kv+6O7MhKCfd+jb6HlV0t1zf3h9+Xeo+KB7W1o/fWDGNugb9yJUnbSfN/L2PfLB5IefkQrZ1LKrBvXMtYzhJbb/oy9D1o7vmTvf9yHPb9+RPfyu3++NCvCzrqBz86VSymHANQkvNaFcHQqspgwG43KoQJPOgWtwI5IuD6D3zUfy3bju1MPvPMNGJvISw5meGLJNGqoY13hp7WB5vhB7tGClV1CvdpPvExV1KNPb/PxRDbB6FgfNaGOhKfrBg5eYMceAOGWNH9FsSXpsYMci3+iG9jp/IDdwO5wyNdA7xCKZ2hPyeXzATa0JWqy+2FBNO9KR/T8C42NA6WFk2/EnMOj+7rS3k4mRVvW7ThHgwZaemR/+scnX3AGcTIlX6NRRTld1suBXaiPwQp01u6XrE24uhz8Su7AHavIqoql4rpV8vtMdKMyQ9eYDXcm3Rinb8SkGysbNMmC3Gdor/IT8kDfMHb+4iHd/RtH2vuw8xcP2dD1ID35lrcN7YhEuAmm312t6c7nDH8mur99gz1Ze3O0I92J3cuUtrH7t0+iZ90u6zeeQsvfXkdp44cpl2t/ZR32/jU5cpRdep9Yho7Xk6N47f7fpy0PX9u3eR92/fpxyKC1g5Z7N+6ZiGoz3hhOs9r5lYnrZecvHsJop7mnu03/92LK7jtxkZLe+Ah77nvF1LbSERwJoPl/HoG/d7J1a8/dL6LzLfOz0jcuuR3bv/9HK5JnnkUD6psffA3tyyav95H2PtQtfxieUfV7d9Ndz6N7VWajX/Ztasau/3nC8mvSKLvKEO4Z8K+MlQ2yVOczKxVf3//OZgT3taLzpdX61vPi+wjua8X+VVusTF7a3FLgzVSlp+/v4X7b473KM2AbMbbRxLE0+UVztlKo8wQMjgQQ2LYTnfdnPv6GXLsWVWtfTblc39PLMfxPG+fESFC6Yz16H3856fXAlu2Wh6/t/MuLGN/ZhJE2c4PKVdf7wD/U33TgpA/ua0XXqx+Y+uzYh5tShqWNbTnoefQljK7ZoL6wTZnz8LZm+Dv2Ysq6NyZeG123CT0Pv6Dr86qVwZEMB9lI3L5Fu2tk1Qfoe2ryeu98aTUKuvahZLd6ZWxsw2Z0P6hxLqdgpmDdsfQFjO/YnZHABpSMlY1c4sDNxnCGFfOBXC0PAu6plGS9nK01kBsYLbQYna8jo/kAMx1bZNNuNTeDuDWBOKI8xeFxIZ5ApkfQkJuxsmGDkbZejHZpPwke3NmuGnazf8s+G1KlbKCxVbFZMRQIoqDbgkmidBjrGdIVbSTO+DgA65sOh1t6MNYzpL7ZLvVjm265uH9ri/HCz3gQA9v1ze6djWL36Xj/sGUhRLWOcdTAzg4ERwJpbyf2Ou/bPHltmzpfogUEjQ+PdvZPdG2xo095KBC0ZgK5mPXZRenrD+7unAxvaXD/eMfCXUOCPSm6DikcH+ERCPSPYKi5eyKf6d/akna3jlyujzsRrW1gexuCI4GM3f9ijXYNoGvl5sn7gI01HWnTuq2sbKQsC1lYSdJrYHsbgsNjqnmgd3gA3gFrWzQDfcPGy0guY2s0qnzV/LNwiMQFd96kukzLr/+iuEz7yx+g75nXELz+ElR+cp6p7evNQwZ3d6L1Nw8pvrfv4TdQt+oDtJ53LYDqpPfV7gFmMrCmn94DjI9r7q9Yds2NACBlKNT6F+7FnheAyp8npzWdvLvv471o//0jGDjnZNRffLzuzxW+swKt29dh5o+/mjJaiylOP9aLOdEG71yK4ZFBzfNEb3KbfqodrjA0No7WXz8I34K5mPv9S/WtVGk7P7or7v/23z0M78WfAwoWml5nKnt+erdt6wbCecPIqg/gO+9ajFck5w1G7f3La5j11bNV37fkgULMedTyq6Xwzp6JeTdfMbFuobNQW7o93Dd95P31wLXqaZ6QcEI2/eLBpAg2/aefgBmXnaRr+3krQyOeR9r70Hr7XwEAdQBaz70mo49k9/zk/wAAge5+TP/ssabXo2dX2DW43VPoD69/PL0HNe2vrkffk8sQuOYiVB+3IP5NG9KuJ58Z2z84cX6oqf9H+Bg2X56iPGPgOzT95B7IQEB3GcmN2LLhMmMt4RB0Y532TxQT6NN4gr83/LRcbZCXpdd6pJVC9+L97ho0boVAdyQ86z5jEyxFn75lfJI9B3hGLOxrm+Kciz5tDu62PjzueFf4qZepa0hHy0b84tbflFPlDUYFmjP/BHki7HFGKtOT21AKlWn0mif7JM5FEW3JSsniFphAi76JDPVRPsdtG1Bs0b4ItIVbsc1OpqlG9XvryAuCw/on/LOSDKRXcXMDVjZIUbT52rJwgkohTHOs/d/Kr5Nju4Zi8NjG09uqYClfuFF/YmIzJw9Ktp8QLkm/E9F43BYByCWHwnaT+926L+x0lKpcx8pGTpLYfcdT6Fi+Pumdng1N2PmzB5X7STvdZUYnN0xA1PH3N1G5boXTyZiw/9U19qw4S86JqILmHZi27K9pp7tzeerQrWYF16yb+Du2oL3r14/rDqfZ99Sr4Um6EO6usPem2xWXc+s8AGa1v7oeJa88nfZ6hNcb/0IoFLfv7Si0Nf9M32z1PR/sxI6f/yWu8KN1GKPvjfcPY8eP7k0a11S6fT123/GU4fTq5tA5FhweQ+OS2zFq4cPm0IgzT64Tpdql1ateQNmm9wytMxQIYufPHkRh6+7wNkLuePBndHLVng92puzKBADV7zyP7mXa98Wivdsxbdlf0f7KOjT97mlD6Uibjn2++4//QNuLyhH72l/+ALv/GBPRy+V5PSsbbmXixIk9dwNbd6A3ErY0VvcjyxBs68BoR6puWjZmPmleFH2vTmayVkbRMML/4fso25q6gK87D48saLbbi6mwsjmo4u0X4N/fBjGW3uDE/hfetChFybyDyt0Cxnc2pQynGXt6DDWFu1r497drLO/uG5BRfU8uQ9G+7emvyBO+9cUWuGL3vR27Teqcq6brby8h1NqOQL+xrpGD67cj1NOLrpfej3u9as0yBLbuMLSubJA0eNiCgza4xdiM1Jm+/0S3V9L0MaZseMvQZ8e6+hFs60D1mki5IEvzhq6/vaRrjpCSPZtR8v4KzWVqVj0P//429D29HOM7dluUQp107P/AR1vR/w/luYj6nnkNgY8yO1dJOljZIEUTheQUF4TT+ZXbmrEpx2TqiZ/eC0lhOTtnTlZMQjb11Ug1453TGRhg2znmhq9mFbd+F7vuP+meErrG0+tMezrh7W0Rk+6MP2zMprzPZVjZsFE0/ORwa2/KCEpj+wcxuLsTgT2RwZJSomdDk7HMTONCCPQNOxsiVWnMhkmh7tQh4KzK7wrb91iyntGuAQw2mev+FQoE0bvRWDr6t7ZMhveM0HsuFXS3wjNm7Kmq4XNVhZ79pLkdpfMsgyWV8aEx9G9tsW8D6bYKbmrG2P5B3Wns37LP/kGRqW7gOr7zUHM3RtpNBNVQWbeeMoVVfbxVt6Xje8uQRLA5/IR/vFXfoGKlvEFJqEfnwNzIFxhq7jY9m3iswZ3tCPQ5EwQkqDR5qZ6TIRRCz4YmxbfMXLJ6P5PqvPf3dkIORgLBRL6HZ3QY/u62tPKSvo/36g4L3rtxD/o270safJ9SJvJtHcc2NDaOvo+tDxSSb1jZsFE0BOXen9+bMqTqnp/eg5ZfLUWwJVwh6HvmNXTe9ThanzXWL1N1/b9+RFc/xwkWVg6yWe2Kx1DQkX5Gs+cn/4eW2/6s+n7iE5rY3d7y6JvouPMxDO5U6C6jkFmGxsbRdsff0PyHp3WlLXEVda8+hNoVj+v6LAD0rNtl2bmaaj8BQPtL1s46beXTyeY/PI22O/5m2fqsNNLeh/Y/PIqmW/6Etjv+lrKwPD44irb/fRh77jI/02+m7PvlA2i+VTucsZJ0jr1mYStDT0Dbnl898XdwX+qoXkbzBiP2/fIBU2GXE+ctavn1X9D0nw8aT4AVoW/fXWfqc+O79qDzrsfR+5GxbljpSjzvE0+7aS8vTXpPjI9h2qvmx7WN7R9E++8fwd57X0y57EBjKzrufAztv3sYe36j/55iB7OtIM33v4L23z9i7mEGTWBlwyXU+vOOtxufxExpUGioy5rJ0KyQbfUXr5UhV1NQOnaB1vCT/kBv6onogJiwrXv1hRRVOh7+HvVxAInGe8KFhfGOzEw6pBUK0ekuPnr3uWkxB8vodWT0yWJ0AHqwRflcsDxSXSZZsE3dLT5pVGhSJTPQrnDNaZwYRvOGTAiNJlfaZH+0ApJd3VbGezN3r0ibyRtxtJI9vi/1PSL2nhV9kGolO/L7xOh44y3h0NSGW2Z0b8+W1boOKxukjC0bpJfbc0s3p8+KtPEaNc22lg0jaXDz+alHuuefVd/frusgjQq+HUynIWE/2x6NKhvOa4U0Jl6Plo8LyYb9YgNWNtLQu3EPtt90p+4nXNt/8CfjGxECbS+sgffR+K4ZjUtux567Uzdjqtn3339NqsErZWIVm1ahccnt6H53G/b+7Q00Lrkd+1dvx95/+wMKulpSZnw7brkvHFIyZltt9z+vO519Ty/XvWyuqXnnObTffDvGd1kzbiTTmh9Yhj33vOR0MtIix8bQ8fpG1fdbn3kXta8/Zuk2d/zbPapdnEY/+MjSbdlJSqDpTy+gean5a7hn3S7s+MFdqRdUMbgqOfx3nDRKj0M745/UOlEQHV2zIe11jA+OYvv3/2hBaszrXb8b239wV1oVuP57HtG13HCrsUnirDiu/Vv2Yfv3/6gZYWzf4ytTbnz/Q89j57eTw1w3Lrkde//2hmYagkMJT+Y1vtj2G3+fdreh0u0fouu+NEIux5QZmv7wbMrvt+fel7HnvlfQvuxDBO5L7oYnR8Lff2Bziq5uHuVisZmW3KKWnXH/N/0pOdrg0Ibt2P7D/1OejsAAtwfLYWUjDfv/8Tbk8DAGd+mbAVYOmmti7X9uBQq6kwd0jq7bpLwdPZEoxlJUkCIXemFn+MLc/8SrGH473D+46/6nIQKjKP9Yu4++DIYQ2t+DnkcnC5xSxjSnZqCGnzUPESZC306+VLwnEs5WR5g/XcwMhjVyp01YduT99c4VjtNId6Lex19WfW/g5bdR2JF+ZTA2CaHePmNhT93wuFXF2PqPU/eD1zgB9z/zJuSIsWAFsWR0kLPKNtK5Qfe/tS719l1eAACAgW0tae1jKzLZ7mfeghwcwvBe8919PaP6upn2vKNvLpt0xe6W7hdWQY6MYGDrPtXlh15fNfmPiWs6en9W+/jwTv1d5+TYGHreMxlW1ar8KGY9Y5u2xX2/qNgHpqNrN2J0zQb0PfUq/L3JZTI5Gq5s9L30T83NJj2Ejd6bTVzLiXNxja3/OGn/VH3wGmT/AMb2mysfOjIpqgmsbOQSgyddpmLwZ/3EYtme/nToOKckkitKSctkQaHLEpnM+N0UvjUNjt4r09l3Wb7fyTgj52rc6eGGbsla3aiySZr70LXfOsfzE1Y2LNS7cQ/GB9J4QmTS4O7OuNC60VCIALB/7U4MNJoYDGhhP0Up5eTMrCkuqImwnAYuvNHOfvRu3IOWp99NimwS5Rvogb9HXwuUGSPtfRhpSj1grmdDU9xAs6QwpHqmCtYgQxL7V1sw6ZmFhlt6NNNUtHe7+o3PZAY82rofg7vjQ4EGdu/FWI++p596xHafTGwuN7yuJu2m/aHmbtOhk62nL29I6rahwskxC0rnnb+7DYEu811IRjv6JgJyDG1PHWI4+mQyNDaOnnW7Jl7v/WCHZeF1YzZm7fqsoJEmreSa7XYyvn8yPO/Y/sHkyQFjFHS3YnzX5LWZ7ngJuwv4Rlqpx/badz80y2iI93T0bd4HEVDIoxIrZf2Dqu9pUY1iqdbKmtt1DficTkCuCI2No+POx9DdMCPj2275VTi8Xd13rkx6r+veJzOalvFN2xRfH3hBu78lEO52tecXSyGHh1F03Cd0b3PPrfdOdDUafOVtLLjzpqRlpr8QDj3ce13ye1ZovvUeVOpYrvOux9Ezbzbm/uAyAMCenz8AOTqK6sWfsyQd7S+tRf9zKyxZFwBLuiNphX0ubtqCmlXPoW3KpzH9wkUTr3tGhhAqKtG/7QnhjLz/3kfQD8SdC3JwCM2/eggH/Nf1JtabrPmeyTFTU996Ev3HfMmS9SrZ98sHkl90Y8ExRuWKp51OginTXg2HCG++PEVeoXK+d//3ZCjS3sdfhijVdx7v/ctrcWMwep94BYOH9wGHnqTr87lMKQJdz7NvmlrX6Or1wFfPBoCJ+025wj0DAKZ8mPq+FSfmnBAi5l8XXqtDb8bMNO+S9HXc+RjK7/guPAX2F03bf/ew8huJlY1I93ejFcW61x/BeHl16gXd0OqVAWzZsEj0CVSozeKnBQYyAaP5hRV9/RKvj7iuWUa7dYUk5PCw8c9aNaYhQ4Ktk+dItB+pngxHT14U+9Qu6fMqmaWe9WodjXROI+9wuCUq2BOfbjFuTaSfRKHe5CfWZp82BtvjWxosbdU0cOOxfwZxcwe4QKHftNH12/0k2E1dSYKdyWFsRZ+xwcwAjBdaHC7k6JozbyR5jGFof0/a256439gobvdmaF8rbsYlFYpUbG/9SXUMVAaIO32dZDtWNkiFjozJ6szLpRez/YU5nVy6f+wQ3edZ9ZWzKrGppXvTlzorKVk7ZsMqWjvADemjtFkePpVyxkQ+mePXOisbFuhfuw07b/q97duZ8fSdaa9D62lQ35PL0PL0uwD0FQCK926Db//k08vWZ96Ne3/Hd/836TNxoRptGrA2tFd9crnRXS1oXHL7xNiO7T/8P7Q+v8b0tjxjI2h4LDkUoROixy5W4rgFI3b/7hnN9xuX3B6e1VzhZGm6S394YwDJ69DIeNVu3KGxcYxaOCbDSbquBZtuTo1LbkfjkvhzetevHsXuO55C45LbEYqZnKvyg9cnlt/9R/WZxrvf3YbGb/1WM7Rp2VZrZ4bXIgORdLj8Bp/Og46KTasw/YX7415recRgtyAFqUKQGtX8s3sRatUe79b3zGuWbrNxye1xeWPTnc+h6Q/PpvycHA+i8Tsx97U0W5EyOSu1mUp978Y92PWd2+EZTd0C1PJ37ShPlkmj94QuGhVDrc11r9qK7d++Q/92Es6F2H8Nr0thfW7DyoYFhleaL6wa4RlLccFbcOENvvK2oXWV7Jicg2Dg5bfj3lObFV2NVZWN3vfVQ/aVbfsAANC/KTwQTfYPYOD5Faa35d+vf6ZtTRb025w4djF631EOj6y06USBzY0pCzs9K5VD245t2Jxyu5pM7IfRTvUuZDktAzeZ8d3NCGzdEd5cYLLCULZtsoIQ+Cjhuos5sXqeexsIhZQLV5HlKte9bmGKUxgPz46eVp7j8pt7xcaV8A3EP3gZee/DpOWMfg2lEKTpylRkxFi9qyZD4I5t3IIxlfGGsYIDwxPnjhFqQRD6PtQOLGH0/NS8bRvvZ42eZeFxHQVdqQMdDC5/x9j6XUtlP6U4R3uefdNQmSdpPE/M+nv+8ZbudWXLpKCsbKTB5feaDLFwJ2TZ2AvTFE4c0/lFqg86EYrVANXKjNbYFaMFxFTpsiEuvF5Zcp8gO0VPAqWTgTcZSyjmGSYuvnQPR1I68uWeZ5cMZqCmHkyYPWFy8MbAykY6DD65zxYjbb0KERmUu6cIKbF/zY64cK5m9azdofh638cqIeRUhAbVW4CiA5IN0cgw/L3K3ZSGdneovidHRnTPOp+uuAHjKt8jNJ75G16gL/4YjW7dHReWdqISkiKzHmzqwsB29UkiQ4Eg+tds0Z2ukfY+9G1KDkOrZ2bjgQ+3p54sU6+Y750y/GmKfdT97jYMNnVphmb29e+PD8GsQ+lO9ZnVk3gmn96p7eM4oRCKm7ZA7WFGYUczRju0u6AM7pz8vmrXvVYBoqCrBeOdPdrpdKFsrp+M7Juc1K9r5WZ7v0sGC3RCpeU61bU9stPYNTm0owUlTZsNh0wWApP5qIauf26ZDDmstv80DlrPhqa4yeu6VyX3Quhdvxs9G5oQ7Eue5G6wqcv2E1wODhquWPSu3216e9HWRxkMoeuf+u9V2cbW+GJCiEoA9wI4HOG7xlcBbAHwKIC5AHYBuFxKqd7J3sWCLakvznSNrtW+odvR57P5Z/fCf9B8XcvKvn503fcUehfMTXu7PY9MhhKNzVDaf/8IKlRCEyoZXrkGOOw0xfesmO05llrXj4G7HsQ0AH1fU0538/0vY843Pzv5gp4bn4lMdmx96tlyO//xjumMwGw3lD13PIEDfnr1xHcKdXSi+bePxaxY33pbbvszACiGOwaAlsffTu7eo6H51nsUX997/8uYveRCzc/GjUeyUPuL6XXT7F6aui/69BfvR9uLUA0BqqRkl7nZ4ZP2scK5X7FpFSo2vQO1IlPt64+i63WBqju/r7qdll//ZeLvkt0q3Qk1zrO65X8L/3Gh8j7R3fUnw121Qj3K9wSr57KxQ8/DL0z8vf8hg+O+DBLeDD5rVZlnI1X+abSLdukzf0MpgIKqXqD8eEOfbb39r5rvF7XsxP63nkPBoQsnXjNaOO6863GI8vKJ/7sfTB7n1f1n9bGCLbf9GaKgwNA2zWh/+QNMO//o+BelVL1Pd/zpCXgqpyS97lGax0NF1z/+ibFN2yB8XrZsmPC/AF6SUh4M4BMAPgZwM4DlUsqFAJZH/ieTQmPG+4/qovNkj4YoDSmEbSR1oW6VkJYO3PhDvZkf6xDq7E56Tca+ptG9wEhkl8SQumYF1Y5XunRcZ+O9yU/4so+xSc28Q3qOW/rXiptC31pVwJABlXuCiyoVrmBH6He180ltWzZ1oxIDBvM9HfvCMxYO7R2bpwYHjIcOlv0W3m9sKpQrtaqYunwMHN/ofg0NZX5i6EywrbIhhKgAcCqA+wBASjkmpewBcBGApZHFlgK42K40UAbwBpYxirvaBftfeJS7CGQLVxU4I+LSlKkxJ2rMhu2MKQhoVhAdfIrnmrDWarL0mnIdpXFyToSjTexGlcm8x6rrjOekPXJ8v9rZsnEAgA4ADwghPhBC3CuEKAUwTUrZAgCR33U2piHjYiO16NX0pxdSL6RD94vJoU9N05sxRS8QqwsMKutLDMm5+z+1m37V9Dz8QtK6UiVn2ktLUy+YYGxvh6HtaOY3aWZGsTe23b97BuXPqcygqrBNy7PB8XE0LrkdIqj8FFZAomTXJs3Zx9teSOhiYGOhVQ4OTYR4bX0uHI1HDqU3Idh47yDaf/+I6c+33fG3tLY/2NiChsduR8Njv1FeIHrs+/WPc9q/ZnLclWc0eZyXWuE+8dQu3WVgPEga0inspZwcLLqNVBPHaZy3xfsa0fDY7Qg8oD+fC+5rVXx9x4/unUxTIICh5nBLYs9LqzTXt/17f8CUDcmR7rLJ9m//Num14Y3bDa3DnxDZS6/Y06TnkRfj+/fbOEB8xjN3xb+Qbv6Y8PnQ/h70Pb08vXWa2G7suLhg8z60L0uOsJbKvkeMzz7f8cdH0f7YCtX3lfJJT8BcK0WoK7nlPxU3PjSLZWdlwwfgaAB3SSk/CWAQBrpMCSFuEEKsFkKs7uiweFZul9HTr16PwBZjmacWvfmSkM5G0zBzURomJaQE/H3G56wo3KWzT+vEDteXYUwsbvIGEtjciIKufaY+a6Vo0zyQ0AdeSkz5SDtue/9zK+L+t/MBeezM4wMvhOcZkCPpNXcH91iz/80+nR9cHR3HYN1Nqvc15T7mUqXPOunj35/++MDE7it968IVw+Be7UHIcnQU5R9b+CDLJVJ970TeQWNdKePyo9gw0K9Nhos2OpBbLymVK/u5qP+FtwwtL0MSQ2++b2pbWuGRjYb6V11PjmaRdlY2mgE0SymjudQTCFc+2oQQ9QAQ+a0YIkVKebeUcpGUclFtba2NyaS05OqVkWFGC8qu2u12lPKldNmXdLFs308Ozq7shspPug8OKLvEjalh6Nv8k6fXuW2VDSllK4A9QoiDIi+dCWATgGcBLI68thiA9jTF5AjdE8VECzomMk05MqI7moUMSXS8ZjzaT9/6XRmdpTVRYbty9KtgW3xr3VhnJI2jY+h8y3xL19iOFCFFExS27k7Rdcvem6EITDaJi9hzzkwUnoC+J0uJ59y+vyyPC8eoh5lz0W0KdqWexMyo4H7lp79aM0QHW9oNh92N6nh9I3o3phFhLo2KWuI1DJgLrT26bpPlT7j1THA5vM5YJKHq916CdyD10/2B7W0YaGxF18rNGB8YQccbmzA+NIbmpcvRvyX91jwZDKHj9cx0s0vJxPkTW9mwq2XDMLX7feT1gu5W3aGura7AD32oP5qgHkYGqKcM0W2haMt+XLh6FcXN1ufddrM19C2AbwN4SAhRAGAHgGsRruA8JoS4DkATgMtsTkNWE16vZc1zdoh24YjtZqKXHBzC/r8+p2vZjuXr0ffUq4a3MfbI37HX6zX8OauodlVKqJxFv9v4nn3oeXgfRs6qRnIgvdSMhmOuffMJjC04zMSWkpmZBVitb76ZrkGdTyf3Kx/bmFygSjznRj/4CM3NrTjgZ9fo3lbvE68YTp8hsfNs2PT03TOW3pgTJbInRWFU4RyRg0No/19z4096H3/Z1Ocmtm3xvq171dz3aH32PUvTseend6dcJrivFcOt+rsGlez6SFe449gQqj2P+SEDAfQ+Gv5/5N11hsIrK2l7ce1EV8asFHs/V5v7KN2IREbz4hQPCys2Tc4OnunZ3oNNxubZSlS8ZyuGZx1o6rPtf3g0rW2bMfiqdvdhAKj5Z+pw5m5ja2VDSrkOwCKFt860c7s5xeu1b/JAK5rzMpTxBAeNZb5x3f/T3X8OdFPxBI0HGjAr3a9nVVSXxDEbRhMWHDDfR1mqzE3glGzvGaXGdd/L4gR5h82F9Qz2O9O/Xo7b+yDLTMCUVJzaV3ZQbdnIcPcqKy8DR6J8aTAy10VGWbTThXB9TD0AnEHc/Rx6Ki+MdqOymstKJW7rZum29FjOZcff1bJpX7ktrW5LT4a5YcxKTlE5n1Tza5eM2bDyfsJzSp/EU0VvdLtsxcqGGVIaCmeaFo8zh0ip+4miDF0gqhNVZcjeB6zvNqN1Dkkk5/7df34G238QH87QSESpnd//neLrPoNRVmKNrPpgYhZYSzNLjZaN0GggKVx0eF+av2PKQACN3/lf05+3XMx3H1n1gTNJsKHQkG64Xiu1PvueZd0kQoEgqv+cxj1Bx7UTDbnsRpksYLrpQUvXfU/F/d/zyIuKy6kd3pH3PkTjktvRvDQ+hOz4jt0Y2J5+BLI4Gjtu4OXkLqiqwzhyvFAMAENvvIdAn/XdTGMltgApjQHLJXaP2chNmXwa4bImyUSZCn0bGrT3wk+5/fUZHhCsktPLQeu7EBS0N8Nto4K0GoaDvf0Yb9yV/Jl0L5VxZyu0lFkDLxkLmaklODyWeqE0Db76juUt3ZZ1gbS5O1bctnKwrDvy7rqk1/rWNlq6Dcvm9MuTlouhPV1OJyGnsGWD3CkxZ8y3WYbd9PjOCVK6f3bndGmVmoyUqHKx9JUBwu93OgmT9BxDG/IEKwqOuiMX5gIT35WXp83sOv944CzFlg0DOt/6GN7hWQgWFGdsm0Zm7zVqYF36T058/TZNqpdwodvdjapv8778zVyEQHRit54PdppejaW7L8ePha9/P4r3pT8JZ2g0gIrGdeknSEHXq85037KCnkK03sHL3e+mDjNpydNel7diqxFSouNV47M4Z6Oqlx9JuUwoEITHH98Clen6mBXZ59D7HwG+5CJiqMP45La2SvVlTe78/S+8k3ohE6KtWFa1ELk5WmksVjZ0Co2No+fhF1BbWonW865xOjmWGF6pPNuvG4ztjA93N7rW3rjq7b972Nb1G+bQ08LOe550ZLtJTNwtgy3qczm4zfQX79d8X+/Xn/rcn+EdsieS1vDb7h0jkErX2+bnqknUvTQDYSZ1HnA5bG13Uiu6UY1u3pnz/c2jfIM9KZeR40HA71y4davkyzFVM74rjfl7dPL177duZS5/QMduVDpFa6FmJm0iE7Kktm4XpQHirmdhZidgPPStzKUxFzq/u10VjWwXGs1c6OhsZkk3qlH7x6tkk+ilm+7zorQqgkr5R6YeYLm80OsmIpQ/5ZyUlQ0hxDQhxH1CiBcj/x8amZCPyD5u6gfsQOaZ0a/vpn0dZWKf50OUFCIiM9w2/4Vl3Hj/oiR6Wjb+DOBlADMi/28FcKNN6XGt9pfWAgBEaBwNf7/DsvXuX7PDsnXlFIdC/iop6GrJ/EYtyED1zvQaHHdHrPdYNf98Vr3CkSfRUABg1/884XQSKANG3l+fchk56s7JyYxejYnhu41v0OXXf+J4w2AIo+s2Tfwfas2e7p7ZQI6kOdt6jnD7ZaGnRDdVSvkYgBAASCnHAddFyrTd0Mq1tqx3YI3O+SzyjJuewhS3sEKYDfRWrrLJ+I7dTieBSJPRFkU7wne7WSgQX1zKRD6ltIl8CVlL7qSnsjEohKhB5AGGEOIEAOZnActa7in85oO8CqeoxILvr3sWeKvkYGHf/fL8OiFyG+aDREn0RKP6PoBnAcwXQqwEUAvgC7amivJexgvKGjwjg5nfqEZYzqHmbuzf3Ab4DtFcRaaf9Ae2pB/KNZZnzNmJHJ20f8WHGKitdDoZead/o3MtSUoTVWaDUC+DFCjxdLShYLgf4pi5Gd92aMCZ1qP2V9Yh2OfA/VJDWeM6DE+f53Qy8l7KyoaUcq0Q4tMADkL4MdoWKSVDfZC9rKhsZPETpsoP31B9b98vHwj/cbl2ZYOy1/A/1yJ/q1oWMJl/BB8zOUYmi/OarOOiB1FKoqfCtFf/Gv7johvNrSiN7zm00doHP3r1Pb3cke1q8e9vw9SVzzidDPu5PA9KWdkQQlyS8NKBQoheABuklPkz0smmMQQuPz+c4/Ibit08AXcOBiUicpTbb5puT18e8oxxELnT9HSjug7ApwC8Hvn/NACrEK50/FxK+Reb0pYfmDEpS7OyIUMSCLkvyhJZgNdMDO4LyjO8/skoN54zJsonMiSzNsvXU9kIAThEStkGhOfdAHAXgOMBvAmAlY00jK23bqZbmlRx329Q4XQi0uDr60q5jBhj6weRGzTd8ienk2BK6x+1u411v9eYoZToN7xyjdNJMMQt5dz+f7yeeqEsNT6ofS/UM/N7pnneWoHKqQ2GPrP9W7+BsU+4h55oVHOjFY2IdgAHSim7AXDsBtnDLTm0i3mdGLhORDlD9g9ovj/4ofsqG0SJAr3ZGU65sLPZ6SRkjJ6WjbeEEM8BeDzy/6UA3hRClALosSthlOdY2Ugtz8e1EBG5DeezIEqmp7LxTQCXADg58v97AOqllIMATrcrYaRPrmZswX2tTifB/VjZICI72fTQp+XJd2xZrxt0vrIWnpKiyRdM7sPB11ZZlKI8wHshgsNj8JUWOp0MVSm7UclwsP7tCHeZ+jyAMwFwoIFL9K9zJsQdOU8KPb0gcxBbvSgFlj2sYdelNvjqP+1ZsQsMrXgXAy+ohy7XjQFOdBva2ZZ6oRzX9sRbTidBk2rLhhDiQABXALgSQBeARwEIKSVbM1xEBpkhERGRDVixpywgx4NOJ8FxMjDudBI0aXWj2gzgLQCflVI2AoAQ4nsZSZULpRpIpyYU4EVANklVEBh3d+ZD7hMcHnM6CUQ5JVe7OpO7yGF3zyWi1Q/jUgCtAF4XQtwjhDgT4RnEyYAd373D6SRQjhLZGnCbXGvnTb93OglEOaXlzy87nYScxwY4YHzXHqeToEm1siGlfEpK+UUABwNYAeB7AKYJIe4SQpyTofQRkRrmsETKOGiD3GLrFqdTQOQ4PQPEB6WUD0kpLwTQAGAdgJvtThgRpcDKBhEREbmcoXA2UspuKeX/SSnPsCtBZMzgspVOJ4EcUvFR7oaP1OL25mJyXu8TrzidhJwQ2Mxoh+R+4129TieBUtAzz4ZpQohdAPoBBAGMSykXCSGqEY5sNRfALgCXSyn325kOolxUsmez00kgohwmxxgwgNwvl0Mp54pMBOo/XUp5lJRyUeT/mwEsl1IuBLAc7JJFRERERJSTnJgV7CIASyN/LwVwsQNpICIiIiIim9ld2ZAAXhFCrBFC3BB5bZqUsgUAIr/rbE4DERERERE5wNYxGwBOklLuE0LUAVgmhNDdyTxSObkBAGbPnm1X+oiIiIiIyCa2tmxIKfdFfrcDeArAcQDahBD1ABD53a7y2bullIuklItqa2vtTCYREREREdnAtsqGEKJUCFEe/RvAOQA2AngWwOLIYosBPGNXGoiIiIiIyDl2dqOaBuApEZ7J1Qfgb1LKl4QQ7wN4TAhxHYAmAJfZmAYiIiIiInKIbZUNKeUOAJ9QeL0LwJl2bZeIiIiIiNzBidC3RERERESUB1jZICIiIiIiW7CyQUREREREtmBlg4iIiIiIbMHKBhERERER2YKVDSIiIiIisgUrG0REREREZAtWNoiIiIiIyBasbBARERERkS1Y2SAiIiIiIluwskFERERERLZgZYOIiIiIiGzBygYREREREdmClQ0iIiIiIrIFKxtERERERGQLVjaIiIiIiMgWrGwQEREREZEtWNkgIiIiIiJbsLJBRERERES2YGWDiIiIiIhswcoGERERERHZgpUNIiIiIiKyBSsbRERERERkC1Y2iIiIiIjIFqxsEBERERGRLVjZICIiIiIiW9he2RBCeIUQHwghnov8Xy2EWCaE2Bb5XWV3GoiIiIiIKPMy0bLxXQAfx/x/M4DlUsqFAJZH/iciIiIiohxja2VDCNEA4DMA7o15+SIASyN/LwVwsZ1pICIiIiLKVUIIp5Ogye6WjTsA/CuAUMxr06SULQAQ+V2n9EEhxA1CiNVCiNUdHR02J5OIiIiIKPv4jzzE6SRosq2yIYS4EEC7lHKNmc9LKe+WUi6SUi6qra21OHVERERERNlvyslHOJ0ETT4b130SgM8JIS4AUASgQgjxVwBtQoh6KWWLEKIeQLuNaSAiIiIiIofY1rIhpfw3KWWDlHIugCsAvCalvArAswAWRxZbDOAZu9JARERERJTLPH6v00nQ5MQ8G7cBOFsIsQ3A2ZH/iYiIiIjIoPID651OgiY7u1FNkFKuALAi8ncXgDMzsV0iIiIiu3in1SLYxiA2ua7giIMxtmGz08nIWpxBnIiIiMgE6fKQo0RuwMoGEREREZGKsk8udDoJWY2VDSIiIiITzE6mVnnlBRanhOxUfthsp5OQ1VjZICIiIiJSwd5y6WFlg4iIiMgET3mpqc8JD0uvWYW1jbSwskGuVf7Z051OApGjPFMqnE4CEanw1k/DjOvON/VZGZIWp4bIvVjZINfyV5XBt2Cu08kgcoynttrpJBCRitJPHQl/eZHTyaBMYMtGWljZINcKP/nhBU5ERLmF3aiyC+sa6WFlg1yNGTIREeUadqPKMqxtpIWVDUqy4M6bMOvnNzidDCJigSQjik86Jq3PextmWJQSIqLcw8oGuZeUfJpAREQ5h632lE9Y2SAiovzGhxqUYexGRfmElQ1ytwwWAkpOP8HQ8t6Z9TalRD/h9TqyXd8sdhshd/DU1qS9jnSfMrOuQkSkjpUNoojpFxurbPhqq2xKiX7CoXkYpErpShQXZzglOU5m9umn/7ADM7o9a1hQ0mdtgTKM3aiyi/CyuJwO7j1yLRly95gNNoMTOc+KQpta5ZmICGDlMF2sbGQh3wFznE5CxvimVjqdBEWeqsqMP3V2kymnpxe9J5NKTjve6SRYpvSsE51OguuUnviJtNeRbjGClZX8lM5hLztopnUJIfvxGk8LKxtZaO7/+4LTScgYT3FhxrZl5MnFAf95nTsqGw6koeCIg1F9/MKMb9esGZefjClfOEdzGf+BB2QoNenR6upX+/X8yRdilR9uwcMXFiQcVXrmp3Qt51sw1/Q23NZFsHBqudNJIAPc1LIx8yfXTfxdfNIxWHDnTQ6mRh9WNojMCoWcToEzWDDLnITKpJtueLmE+zVLBMadTkEcNzxvovyTjV24Wdkg98p0Tm6wEO0pK7EpIQbSUFPpdBLIJbylRU4nwRGeAl/a6/CWO38tZzOR5gMIvYUnz5RyeGqq09qWlVhJJSd4CyfzvGzJu1jZsIHept7iE4+2NyFZzsk5/QqPPjzlMnUXfQoVF5+ZgdSoa/iXCzO/Ua2Dwkd9hkMoW6Vs/rS0Pu+bOyvtQmOmVV11IQprytJeT+WxqbsFFh5zhOb7Uy46Le10ZKuZ//4127dRvfhzmLn4LDTc9EVTn7fl3HYo9Djlt9gueNM+s8jBlOjHyoYNRGGBruVKDp1rb0LSoTNjtnOeBwHnahv+6alj9xdUlaLunKPsT4wGX2khio49MqPbzMqneRmsBBXNnT7xt/D7M7Zdwzzx2X/RggaHEmJezYkHWbMiHflM2VELNN8vPTD79p8VhN+Pojr7Q3BXH78Q3uICFFRmx5PcKDe1xOQyb316D1uyVbaE5M2OVJJ7+dLvwuAWcYXoLHvCm1G5uG+s/E6xFRsX76tsa8VwmlYlW7BFj4hIFSsbBAAQ5ea6IpSdrS+KiBnlh812rLCmtVn/IeYiMRWflD3hYvUo/ORhupYrOi790KS2s6uwmO75a2Mh1jvD+SeBerorukaqY5ni/YrPn2Voc97ZxkKjisophpZ3Gzu6FXuqJydeLVo4y/L1C6S+Pr3V2X1cYpVfcKrTSVBVfpp991dRmLmomLmKlY0Mqrj4TEz54vmTL6gUJJyYR6N4UfimL0pLDX2u/Mh5diQHQLhfotsevi648ybM+fbnTH12xpWftjg1DokclFnXn6dr8ZJD52LBnTcZ7lKktzJjB0/tVGtWpHACx/b9n3Lp2dZsRzMJKrO9lyp0R8nwBTfjqjMw/aarMrpNJZnoGlh3trFK94zrjY3H8lRoPzCKu/ekWpeBrj/Sogpx7YXWz4dzwC++OvG3b4qxe5tVlLpVm+nyU/aZ0xRfz+TYz2kXHpuxbRmVzrwlqfbhnF9cb3rdRuh5YOBbYF+Zy06sbGSYnich2cTjt3eAnEx7ui2T3FbL0ZDxoF2ZGrORyS+WdLwt2naaT8OtoDrhnEv6+mbLGKBU6ZTBPA2FbQUps+Y8iOXY/Yms5ZL7fS53x7TtbiOEKBJCvCeE+FAI8ZEQ4meR16uFEMuEENsiv6tSrSuXxIb485W5J1Sl2ac+3mJ9g+HNSvdpFPulW89Xbf9gUCBHAlt5nC/QqwVx8NfGZ71uCOWczVjZSE+2DHQ1yju1cuJvUVAQeS2vij2uIYqLnU6CPhpjYf112Xnu2Hl1jwI4Q0r5CQBHAThPCHECgJsBLJdSLgSwPPJ/VlPsjqC4oJiYCE6UlqL8oBnKyznwhGfKMdqRVtT4K9K7eKu/8lnN96eecggqLjrD9PobfnY9/Acb/252PGVLtU61jDBlKGWLSuV6uk5UX3sxpn32OHNpMVrxs7C24VjFRemYG0hM7KIek33yRZlyhb3+CyfF/T/lk5OzqMf2dTdCqwuonu5S1ddebGq7Vig+RbuLiKdwshugd1pt0vuh8cnKRvHJ9oejFEXGHlbZ/dyl6IRP6l52yhfOQfU1F6HgyEMmXvOVOtsv3jdvNmb86FrL1zvj0hMn/vbUVGHqDZdi5rXnGF+RSr5hxwRv3oZw2SRaOcoVBQcfkNYs9HaLHsvp371CdZls7Y5tW2VDhg1E/vVHfiSAiwAsjby+FMDFdqUhU7z1ddrvz6yf+DuaXxQeOt/OJBmWqSZsUR6ODx0t2HqKUmdmdefqu4kptWIUTi1HQYP28bFD9Hsa4Z2p3I/XU5CZ8KkV56SeH6L62Pm52Y0qUTo38Lh0p7uvYlpCZ6s8nEi5CuXvonUc/XNN9n/WaMkprE3dIlZ9bGbzxdgKfmF9OE9SGyvkKQ4XhkVREUR5fAVOyviWDU+J/a3W/gMN9t22ubZRdYr+wf61ZxyB6uMWwD/NPWFhC+bUo6TB+vQktthUHjUX3qLM5OlGx2BGeavC16qnKosGt+u8X5QcdkDqhRJluIeEr7xYNWhPtrYA2ppqIYRXCLEOQDuAZVLKdwFMk1K2AEDkd+ZLgk6KtGy4pY+gmpwqUJrZhsuPT1aJ7v883KfZ2A8dgC3XpSv3RSRNMiQnv7LKeeormXwwIkfGkt7P925Upp6w52GekBVyog+riiw451yZV6bJ1sqGlDIopTwKQAOA44QQuh99CCFuEEKsFkKs7ujosC2NehkJ31lzbnxzfGz/zCnHLIAoKEDV6UcBSO46o3f24ZJTzUeFKPl0cjeYxBuFVvcob/00FB1/FAo+cajhbVd94UyI8rKJyClGb1CJ4WOF1zsR2aPkTOUwvKYKATZnSL55s21dv2MsvEl5K8shSktRes7Jlq0zkWdKBURBAcqPnzyXrdxexXknpl5IQ/WFJ8E7IzxJoLfc5JgKncdESqD6nEUQhYUoPthsRDyNbXk8aXWJtEekshEMxe2nKV9I7ubiKZjsRx1s3he/FgGULaxP/Igmpa5Yenimu+v5XOlp4ftJ8cxq00/S3c6u72U0vLERRkMtFxw+OUFm4dx6iMJCTDl3sjySKnS7p6YaJacd7+5JDNXu6ynu95mon4R7wEzmQVWXaOeV5ReeNnFvyAYZaY+RUvYAWAHgPABtQoh6AIj8blf5zN1SykVSykW1teYyZSs1XHOWrsFFDbdej7IFkyfAgjtvirtJFdaUYf4d30bpnHBozdm3fjXu89Mv1lfZmHax9vwWpWepF3JmfPGUlHGjtZrq5v3kKjQsPhOz/0U7lOKCO2+a6PsZVX3sfMz/1b9A+JQHrabax6WHzY1/oaAAoij8XYoX2pdxW63+Wn1hY41QKiDFduHLNsLnxfxffx3ln0hu9i441NxcJ0D4vIzyVE3B/Du+jcJplROv1V9sXQjOsoNTzCqtcRfzzWnAlMNnofiI8JgjtWsmFTkW0L1s2fxpmP/bb8FXrjJ+aE4DapdcbiodwiN0d4nMmOgTxIQKWe0ZR8T9v+DOmyaPlULlTUrjYw7m/ftXMPs/v27oMwvuvAmeIu3t1H37CniqKg2tN6pU5YGNlpIF4TzeW+TH/F9/3VQ//1TV4Yz0s9e4Fuf/2thx0mvezcl989UCOqhSOB9rl1yuK9Ryzdcumfh79pILJ+a98RQXYv5vv4XSBeH7hygvw8wvn5b0+bm//tbk3z+5GjMuPxkzb7zMWPojSk4/AdWLzYWVN6Po+KPS+rxvrrXztsy75UuT3XeFQPXxCzXHwE274BjM+/GXLU2DneyMRlUrhKiM/F0M4CwAmwE8C2BxZLHFAJ6xKw2u4+bmu2iGlanmO40bNxmktQ+N7F+7j4WDA8QNs2rbLnhihvFxXYvZnRZ3dg2Y7EaVqrufm7Nvq9gx2JiMUQ1VbYbRay667VBibwDl9Vh5vrgzf4jIh4vfZna2bNQDeF0IsR7A+wiP2XgOwG0AzhZCbANwduT/rKA2gFdN9OmSLxJi0l+VPODH7nkq1HhnOtz8Frl43VrXSDfkrs/guQLA9KDkaCg8f1WZ/shoCnwK56cVfBXm0hTdG9EnxnaELfRNqwlvy8pCVsxJbcUNNN1rxKNzArG47ZjdqMZ+VGst1TNXgdGuQ6kmkIwGcPA1hPNBT4EPvqrwa/7aSuXPRFqWrJx5XSv/j20Rj09Iiv1lICCAWtSxVBMExm2OFRT9dExsqhau3V9dbjpKnF4F08Lr91WqH//YliuPL+aatqBAbvZeAcRHi1NlthtVxipCMm57/nqLJpd1ATujUa2XUn5SSnmklPJwKeXPI693SSnPlFIujPzutisNVpv1jc+idsnlqlECYk2/6SrM+uGXAISbu2q//gVUHZPcHcRb5Me0G79keVpjKYXza1gS31w5ecOYvKj0ZmwzfnQtZtzy1dQLKkm8Mdp8UZdfeJqu5coONBn5B0DdN76Ahhsu0LWsKC9THEOjR/S4TrvwWEz9xmWo/OQ8zLplMep/cDWmXHZuZAP69mfR8Ueh8ojJcSSx3d+mfsNcs3hUxSGpu7c13Hp98nicyLlRVFeBum99Ma7Lodmnf97Z8d2aZnzpNFPr0c3CSf3MfudZ374Y0773ZdR9+4qJgkzZeacAAObctkR5W5qNZSYLl0rp17mu2d+/DOWfPV33pmbdep32+m65GvU/uBoN15+Pum9fgYLKElQdPQ9Tv3GZ6izJ0by64ZsXGRrDp6T+5msAhOdaqvryZxTDAvvLiyCUonsZ3P+13/wiGv79a0mv++bNxqx/vRJ1307uylM4X7n7X7rfW42Vk5mVnH4CZvzoWjTcam7W5/ofXI3ar38h6fVo//iS009I2Vc+cTxj5RfD3WY9ZsddAag58SDM+tcrUXJaQjdPzX1nrGJad8GiuLKKUkWy+iuTM9trzbOVqqu2kth7xdQbLtX9uYZbr0dBZQlqv/lFw9sE4h+EJOaJRcceqV7xT8HsvT2q/vJTTHdbdZvsjKHlEG9xAaYcPgv+uSn6YSPc9zk6yFp4BKYcqd73rvxAe/vVK4Xzi42sosZTrS/sXUlDNYrqDE70ZrYbVZph31L1e7diEsCKQ2YaCm1YcpC5vp/R4yo8YqKiUFBZgtJ5dSiaGX5ir3f/Cn98Zlp08NyJv2MrIWnR2LdFdRWakxVVHNoAb6H+DF9tDgJfXfy1YEfLYuwN2g1hCn2lhShfOB0Vh8yELzLnTPQJpr+iGKJC4dp1UTQq4fXCV1Y0eU7rUFCl3TLpryhG6bw6eIv8cQWcyiNmT6RTqbBUfmA9fCUFyaFtDe6v0tmT36XmpINRNl+5tcQ7y/xDj6ii+ioUTUvOy/0N4XuUnocBUQUzrR0/mZglmAkZnqjssDkp70la+XzpvDrFYAy++vB399dUwFurPQg6cTxjYv6qSSNt/opiFM3R0bJm8j6WqqwCJLcgRPdl0vWtMTGdZhoi6ytu0H+9R4/1lMMaNMc5qG4z5vgkBscpOST1+vyHKI8hVGslVRUzZgMI35+mHG7t2BCnOH8nJHuYLCy4ut8kzFUGjOwJqZZx2ka4c5+brXRZORFf4lM1I2lySR9bVx5bPdzavzGTXHIOJdGTLh6/7OXW8y5Cd/LMjhdxgFPd2dVk7X1DAysbJtRccLzqE5jCGuv7vRefvChl2LkkGpNrKSmsKYNneh2qv3i24vveFP2+9VwcnimTT5pMX0wKGdLUz58CT001yhfoGYeifRPWqswUHnOE4utJs6BH1lFy+glJIW4rrzgfvrmzUFBVCs/0OtRceQ7KFtbDU1ONqRfHh1z1VFXCU1WJms/oi1CmSG8GHlmu6sufUYyyUX7BqXGz/ZpR/eXz4a2fphopbcrRCRO66W6V8Sf16fdURielqjScTiPbVmomrzhC/UlY1Zc/g5rzUoet9tRUo+bzp8a9pnUkY8NWTixfXgb/gSYmsAJQfoh6661Wl5fCA1I/JY+dNE9rN0evt6qrPpP0XvGJR8fN+F155QXwzUnd4myZhOuq8rw0rlGdKi+PdI1UGMheeWV8t02l3WoomlkaBb/qqybTEtvlRynUb9VJh8IzpQLVpx0JACg95ejJNw3ew6JKD0j95L8qIc/2TKlA9aeV8/ckUiaduAWHH4Syz5ym+hFD97s0C92emmrVlrIo37zZ8FRVovxg7es1Wi6ouTIm0qGBcQ/+SEtqVPXiz6mOv6o6OZwvVH3ls+FuajHrKz7pGP1loBT7uvK4A8PH+6yjUXDoQlRcdAaqTgp3e1PqHldx+OQ93H/QfMVIiC6vH7qCuXauPFc6Zyrm/+oG9Kzbhc67/x73nuluEx6PQgSIsJlfCk9P37hyje7VGQ2TKbweHPDTqxXfm3rDpag8ai4al9xuaJ2J6r6mENbO4BO4aKbtqa5CqHs/AKBswXSU/UfyuBRFKTan1S9+1nXJoWUBoPqEA9H9YPLrMy47CQDi9tvUUw/F1FPDGVvs/j5AIf2iqBDzfpLcl9uQmP3rP2g+Alu2ay5Xc9LBqDnpYLQ8tSrubbV+7FHe+mkItrRpLlN19DxUHR2Z9fiScIjN2H2TNLdLwrmhdsOuW/IFFM2oxu4f/nHyRb8vLsTtxDpM3hTm3LYEu2++c3I9RUWQIyOYeu4xaHrjvbhl/eWTXWyirTOiuBjzb08eH6E2OFrpfEgk/H7IQDis7ewlFya9X3L8kai/JHUoUyEil0XM/vaVFmLBnTdBhiS2f+s3ip/zzZuN8Z1Nca95ilJ3z5x1/XnYfuM2yLHkifHilrvuHEDhmvPNm42ZV8WP35h6yiGYesohaedRZhXPsmcgZ+z4mKmnHR59EcDk9VB41KGYesoh6F/5oea6vKUWzGoeuYAKFx2J0dXrFRepWjQfXfeH/55x+cloXPEugHCo30SFU8txwH9Njq0oqKuc+Lvic6ej7+nlhpI35Yvnp+zC6j9oPqqPX4jupZOvxabBiGh+Er3+Gp9fYWo9Siv1H7wAgc2NqZdPyCdj8w7hEYq3PH/DNMz8QeqxeFrlgui4Pq0xXHO+cxF2/uxBBNs6UP+Dq1E6rw7Vxy9UvE6jXaGqj1+I6uMXYrRrIJyG0tKJsLtGykCKhEBBZcnE8Z79rckyidL9AgiPq5r4Pt+9GD0bmtC5aVt66VCTwy2SbNnIUWZj8mdKtFCfPABNZ1QIAxdl3JPYTFzMfMyRWQr724qxN0a3qShFSOm8P1WkzMkuA3ZKNdM5EJ/nRRfTVdnQmz9mOk/NcMQrV5yTbi14Mmy9fVKE385mrGy4UMHM9GeILZxeBU+t/gFWiumYERkQN8V8BI2U646GW40MJvPNUh4sP9H0Gm1aV2kFStdEIdUFF7u/wboQmwDgn6E+uDM6YHiCzu+f7sy6ml3rEm9mKmnylRUlvZW47wqmhrfjn6Y8sDP26ZXittWkWE4pypsWpUh30ae9SccoBcODE3Ue8+jgWf/MOtPHPzpzsvB6dE+GZ+n8Azr45qh3MdEKZmB4UjbDUhdIfLOTB5Zb0cU3eh0V1E/eW/yVFs6ubeQhUhphvq2iN7nRULIFekKZpniglhhC3z89vfu8UdEW6GgeG+2+GM2/o4E8/JF7eTQP1BPiOtbEeuYYC5Lgn6a+P1xwW9clW9JpBLtRuVD9F07CwCcXoO2Ov5n6fN13rkTFwTNQduCMiaZIU+m47GQMHL0QpfOMVX4qr7wgrp+jkukXHY+Bw+aEo7v86Fr4K4ox1tWPovoq7Pz+75KWn33T5Rjt7IccDwKwMba7FVe5BesoOf2EuNnkZ/38Buy793kEm/aaXmf9pSdi/5xpGG3uwOCr/4x7r/bMI02tc/ZPFiPQN4y2B16Ie73o+KMw8u66lJ+f9aOrEegdMrXtqOIZVRgfGJn4v/Lyc1FzSkLoyaPmwvOdK1UjvyVG69E6u6b/4Ctou/OJif9n/fwG7Pnp3QCA+h8ujl94omVD5blOwrky+5avINA3HPdazYkHwV9Vlhw1SKPCHc0DDNFZciqbV4tpN34JZfOnYfzC4xDoG8a+Xz6guvyMH12bdL3OWvJZjLTsh7fIn9TtZfZ/fh3BUX0TEerhnVmP4N4Ww59r+JfPoH/z3rjZ5aNqP30oCqdVouOB5yD7+yden/njr8JbUoiuFRvSSbK2aNc8jafvDdedix03bo57Lambogmx11H/cysAIOX9oeHW6y2PyjYjcs+I7doIAMqdhmygksc3/PvXFHsVVBw8A+LGL6FM17hCbeUH1gM3fgkF1WUIjYdQVFeBolm16LjzMd3rSOcWVTyjCtO//2WUzAk/vJr1nc9juLV34n1fWRHqf3A1iurTmxMk1Xoabr0ezbfek/R63WePx+6VayAKCyFHR01te9bPb0CgZ9BU18PSMz+F6k8fARmS6N+4W3e64yQcIM0u0FmClQ0rWFzwFV4Pyg+sh3YPeHXRQoavtFD3U0OtdOhbePLimHpK6oHEwiMm1h0N4ap1M4x+l8Gd7ZFXzO3zlJWUaDQqh58sFM+bHhcho3BqObxTyhFMY53CI1B93AJ0jgbST2CEv6JY8bgV1NdgRGH5pM+XF8WNcYiVeKwUJyWLtoxEj1tBwWTf9gSGC98qyubVoi1m5unCqZPBIkrnxD+5lDoKhrHU9qdieFKNyobqd7Wo60P02k1Mr9LqlUJve4v8qoXUVGFrjfJNqzFV2fAW+VF51FzV9ysOnoGOhNeKZ6RXwEqkOBg/oauF0iKeAh9EaQnkYHxF3jO9DqHW9tiPq2xY/U2j15HhsOhRGudqSUO1s5MJqqRNKcRwlP4Q96m7KSWua8rhs5LORcC+1sDYSpO3uABl8+JbzY0+oFSjtZ6U51Ua371wanlcvp5K7H72VVdMfLZfYdmiugp4plQg1NunsCLlY+4ptX5C20xjNyqyVdz1bkFBZ6Ip1uYbTVpJdUnriBOiA5atWZlzhYmUk4zprDxMdCGw4XianlyPLONI336j/bqzNC/JBrbsWk+0EsnrOy1KB8fKA2bHweeYDbKbngGt/sMORPXicPQEb5Ef/oXzkpaJzgyctH4L+hGXnH4CSs85OfWCMeLySwsuoGhzvCgqhG/BXNRckxyFJ70N5Mbgt9K5tfDNaUDtlWeh6qoLUXDEwYrLFZ90DCouOiPDqVMRc354Z0zH1PNTh4idWL64AL4FczH1qwoRzxRUXnkBCo+K72pVdMInUXHxmaqfKT7pmORZrFOcJ0W15fDNm43aq89XfL/y6APgnZnepJ5KoRhVGbwGXTFQ1gD/wQtQ89WLAYTDNZd8+jhMvTDcHVErNKlZU68+H755s3WPh6he/Dn4DztQ9/prr0g+H2uvPAu+OQ0obIg8TY6cg3VfPAPe2TMnnjpPXXwhfAfMiWt5qvuScmjzqJozj4K3fhpqPn14XKjv0jM/lZT3F5+8COUXnqb7uxhV9anJPGvqpZ/W9yGN63HKkXPgbZiBqZ9XvkfGUQqx/pnj4Z0xHZXH6T9+5pi75kpOPwFl58Yfo9rI+Zmo5qxPmtqGOeqtu1MuO9fUGrWuZV9Z0UTZoODIQ1D15eTQ2VaJlsfqLp0MU64ni625avJ+UPO1S+A/KBz2fep1F8G3YJ5qRDW1sMHZgN2ossicb8bHBp/zvUuSQshN/1xy3H8AKD7paAy9+b5qZUSPaChX00zGTY8Vm2HN/f6l+j5kJHKKapSs7OIp8GHuD78IIDybfc2JyfMwAJgIKeg28378Zc33EyvnwiP0nw+IdPVL6O7X8BXtSlf8vtJ3ngivB3M1Qkz6Sgsx75YvpRWyteIknfMDAPZXoh2upM/5zkUTf8eGa46GtbQkNGmMikMbUHFo6hCiUdGwnnopdSMpmz8NZT/8Ijrf3JS07Lybr5j4f8rhs5JmHy5bMB1l552CgZfeUtxeYU3ZRLjtWdedg8Y14bEn9Zcmz40TDcluqcj5U3DowrhKUmI3nRQfV+Qt8mPej67UtR6lMSbF06ck5UtWn+7e2TMhe/vDxXOD9yCl+3PFITNRcchlaPzWb+O6XRrpImSn2tMPR+/jLxv+3PTPqM+5EXsvqDwiXNHa/9Dz5hKYQvh6Vg6ZG05MJFT00YdjdO3GiZcnumB6PHEh4accOUdzBvfyk4+yINXOYMsGWULtCWhsmdCSQYLRFZqMRpXy5mAitG4uSrcRKjSiPYdCtnPVE3+Xh7kmsoOd16DVA9oNbHnyzzy/B2WtHOwCZQVWNqziS6+RyHdAuAZuNgONDSHqJN8B8bXy2PxSbSCwEdF1+OemnqlYFIefjBXMSA43qNZ1xR85Dp6CyeOpJ4Rw4vdOm939TVMomK4cIlav4EA4opIoSD3Jmxl2h3tMbLGIHawfv6C5AoHSTLWeWnMTw3kyUNnQ0w1TFBejsD6980aLf0p44HjB7PQi+ijNZO0G3nrlUNeeGuV9WlAbHoxcMMtYiOzote3XEYZVFFkwEaAB/ppIaF2D38kMra7Leu/DdmTJ/gPCrVGi0Lq8U+v+ZFceHVUQuVcnhRePbl8h3LcWtetEFwsOmCX5UCQd0XKf3uWzuQLKblQWmfOLGxAcMT84tuEbn8VoZ7/pJyqzf/yVuPCfTphxy1dV+y5PufRsS6LM+CuKUX/zNSiur1R8f/YvvwEZDEEGQ/CVhDPRqaceioF3P5qY7XjmT65DQWUJdt70+6TPN1x3LkbaPxUXxWv2D7+UMjzrrG9dpBiy16jYaDFqyi88DZXHK3eLskriDLtGhYZG0HDr9fAWW3sjm/njryLQO4SC6rKk8L12SvweE5NSRvL+WT+/Ia6Cmsrsmy7DWM/kOTXzJ9fpns/GO7sBwabmif+NbNeMGbd8FaNtPei690nVZaLH2l9ehILqq1EwtSJ+RncLlM6uQf0PFytGt9LLyH62QtHxR6H2wuN15euz/9/lGOsZwt7/uC/+9Zu/hEB/ct5ecchMeCOzMhtRfdwCFNbq+9zsn12H4HDmWinLF06H+MFXkqK66aZQGJv9n19XXHT2f30jKXRuVOzxavj3r5lLiwlCADOvORvD5x6L7mXh2bJLzzkZ1ScfmuKT2mYtCZcvlEJUz/6P6209xjOuOgPDZx4dVzaIPSZzfrIY40P6th+9dztJLR9KzJe1CI/AjB9d65rubJnAykYaYp9+qIWs1Mtb5E/rJppumFsrlMxMDvsYrZAXzrDuSXTpbPV1qWVE/pl1GN/ZBAGpWlEBwgW3xOPgKymYqLioURvQZZSnrAQhaD+A8ZaXpDVBVya6AIUGhw2HvNSTruIZVSieUYWRdoWwgRkkEBn2GCncGL1peIsLUBxTgdE6JxN5ykviQiArxfW3UsnMKgR6BjWXiT3WVoW9VGK6EBphZD9bwVNcqPtaTTwnorTydrP7Wu/ntEJT20Xv+Ay91B5yad2vJwKR+P2a4Wzt4PF7UTq7Bt2R/33lxWkXSrXKF3Yf4+j3iRV7THxlRaqtHokyff2qUcqHvFUVCDapTF6oUAk2U97L4oYNdqMiIuuFhp1tZbOdi5q1Vbt4EeUbi67HiQcfJscGmt8w+/vbys7964J7gZuxZSMN5Yc0oOfgBai9xHyEJy1VV12I0T3aXWrSUXbeKRjZ2gT/TPueRNZ++Rx0Pv22JTOnpkUjylT1NRdheFty82fFRWcgNJ7+zabo+KNQenhymGIl0648E+2PrUDFYbNSL2xS5THzsf+h1MuVXfBp0110UoXYVFN49OGoOCG9LgNWmHb959C9bA2KD52HQPv+5Pe/9ll0vfgeiqZXZj5tl30abYFxVJ17HHpWrEs7DXVf+xy6X34fhbXqLVHlB9YbzutqvnoxhjY3pZW2bDX1zE9gdMdeTD3naKeTokv14s9hePs+p5ORNqPlvanfuAz9721Oen2iG5VKZaPukpPRNjyCquMMhJ1OwZ9wfdVdfCJa+wbiQgCna+oNl2JgXaNl63Na8YlHo/ggneMeMkSxPsNKJCsb6fD4vXGhFq0WDldqX9/8cJhc5VC5VimdXYNSG/eRXlrXevVxC4DjFiS9XneuNbHIGxarz92QqLi+EnO+e7El21Wjt8vX9AsXmd6GVlc3LbO+Zi7uutXKFkxH2QL1+Oyl8+pQusTiOV50KqqrwJwbPw9AZWZxg8rmT0NZiu9iJq+rWjQfVYvmp5O0rOUvL8Lc71/idDJ0qz5+IWAgJK/bFC46EqOr1xv+XOURsyfCo8aKVjbUJtYrqqvAnO9Ze3wTr6/CmjLLt1F51FxUHjXX0nU6aeZVp6deKNOUChvptnrkQGWF3agoP7io2wsREbmXc6FvyU6ZDlluVR0hB+oarGzki8JZ4a5ShTPTG2CZrTLx/b2z03/KTET5zWwI5HxWNDfcTbdwenKQEjOsqmz4Fsy1ZD1kjWg5IFMKpoXPx8I54fMz7VDSWfywlN2o8kTNSQejeE5dWhGvslnNiQeheHatrd9/9o2XOh5+WK+5//1NS8ajEJG15vzblzA+OOp0MtIy57YlGd1e7RlHoPTAmZbl71Y8AW+49XrHw7RSvKmfPsy+lStUBCoOmQnfj65FSUM1Ko9daHuYcjfL32+eh/K1ohFl9/f3FvktC4FrN72hBokos7IpH1GTThh4s9x2fzMa+ptyU/S8tGKesWzGblRERERERGmyZVxIDgzaYMtGlqu46Az4Ks1P8OZGpWd+CiUH2Rf6law3/WsXouul91Fy6FwEuvudTk7eqvj8WfCWqE/uOf3LZ6L9yUJUHn1ABlOVWvU1FyHQ2et0MijLlJx6LMqPtieKVsnpJ6Ds8Lm2rDtWxSVnw6swmSNZp/yzp8NfY29L0/QrTkObz4uqY5MjW6Zr2iUnoWU0gJpTnA8LbxYrG1nOqvCsblJ/6YlOJ4EMKq6vRMO15ubWIOvUnf0JzfcLa8ow6/rzMpQa/aoVQk8TpTLjilPtW/dlJ9m27lh1Zx2Zke3ks2nn2z/fTUFVqW15q7+iGLP/5Xxb1p0p7EZFlG2yOCIFERER5RfbKhtCiFlCiNeFEB8LIT4SQnw38nq1EGKZEGJb5Lc1seqIDPIf6K6uJKSfrzTcVajgYJceQx8bjYmIiAB7u1GNA7hJSrlWCFEOYI0QYhmAawAsl1LeJoS4GcDNAH5oYzqIFM365ueyPsRkvvKVFmLWf/yLa0NLzvvVNyBDbIEiIiKyrWVDStkipVwb+bsfwMcAZgK4CMDSyGJLAVxsVxqItHj8XtcWVim1wpoy18706y0umGh9ISIiymcZuVMLIeYC+CSAdwFMk1K2AOEKCYDMTulIREREREQZYXtlQwhRBuDvAG6UUvYZ+NwNQojVQojVHR0d9iWQiIiIiIhsYWtlQwjhR7ii8ZCU8snIy21CiPrI+/UA2pU+K6W8W0q5SEq5qLa21s5kEhERERGRDeyMRiUA3AfgYynlb2LeehbA4sjfiwE8Y1caiIiIiIjIOXa2bJwE4GoAZwgh1kV+LgBwG4CzhRDbAJwd+Z+IUig5ZA4AoHjWVIdTQkRkP9+82U4ngYgsIGQWTBC2aNEiuXr1aqeTQeS4QN8w/BXFTieDiMh2oUAQoUAQvpICp5NCRDoIIdZIKRclvs6Zp4iyCCsaRJQvPH4vPH6v08kgojS5M0g9ERERERFlPVY2iIiIiIjIFqxsEBERERGRLVjZICIiIiIiW7CyQUREREREtmBlg4iIiIiIbMHKBhERERER2YKVDSIiIiIisgUrG0REREREZAtWNoiIiIiIyBZCSul0GlISQnQA2O10OgBMBdDpdCJIFY+P+/EYuRuPj7vx+Lgfj5G78fjYa46UsjbxxayobLiFEGK1lHKR0+kgZTw+7sdj5G48Pu7G4+N+PEbuxuPjDHajIiIiIiIiW7CyQUREREREtmBlw5i7nU4AaeLxcT8eI3fj8XE3Hh/34zFyNx4fB3DMBhERERER2YItG0REREREZAtWNnQQQpwnhNgihGgUQtzsdHryiRBilxBigxBinRBideS1aiHEMiHEtsjvqpjl/y1ynLYIIc6Nef2YyHoahRC/E0IIJ75PLhBC3C+EaBdCbIx5zbJjIoQoFEI8Gnn9XSHE3Ix+wSyncnxuFULsjVxH64QQF8S8x+OTQUKIWUKI14UQHwshPhJCfDfyOq8hl9A4RryOXEAIUSSEeE8I8WHk+Pws8jqvIbeSUvJH4weAF8B2AAcAKADwIYBDnU5XvvwA2AVgasJr/w3g5sjfNwP4VeTvQyPHpxDAvMhx80beew/ApwAIAC8CON/p75atPwBOBXA0gI12HBMASwD8KfL3FQAedfo7Z9OPyvG5FcD/U1iWxyfzx6cewNGRv8sBbI0cB15DLvnROEa8jlzwE9mXZZG//QDeBXACryH3/rBlI7XjADRKKXdIKccAPALgIofTlO8uArA08vdSABfHvP6IlHJUSrkTQCOA44QQ9QAqpJTvyHDO8WDMZ8ggKeWbALoTXrbymMSu6wkAZ7IlSj+V46OGxyfDpJQtUsq1kb/7AXwMYCZ4DbmGxjFSw2OUQTJsIPKvP/IjwWvItVjZSG0mgD0x/zdDO9Mha0kArwgh1gghboi8Nk1K2QKEbwoA6iKvqx2rmZG/E18n61h5TCY+I6UcB9ALoMa2lOePbwkh1ke6WUW7F/D4OCjSNeOTCD+Z5TXkQgnHCOB15ApCCK8QYh2AdgDLpJS8hlyMlY3UlGqyDOGVOSdJKY8GcD6AbwohTtVYVu1Y8Rg6x8wx4fGy3l0A5gM4CkALgNsjr/P4OEQIUQbg7wBulFL2aS2q8BqPUQYoHCNeRy4hpQxKKY8C0IBwK8XhGovz+DiMlY3UmgHMivm/AcA+h9KSd6SU+yK/2wE8hXC3trZI8yciv9sji6sdq+bI34mvk3WsPCYTnxFC+ABMgf5uQaRAStkWuTmHANyD8HUE8Pg4QgjhR7gQ+5CU8snIy7yGXETpGPE6ch8pZQ+AFQDOA68h12JlI7X3ASwUQswTQhQgPFDoWYfTlBeEEKVCiPLo3wDOAbAR4f2/OLLYYgDPRP5+FsAVkSgS8wAsBPBepDm1XwhxQqTP5VdiPkPWsPKYxK7rCwBei/SnJZOiN+CIzyN8HQE8PhkX2Z/3AfhYSvmbmLd4DbmE2jHideQOQohaIURl5O9iAGcB2AxeQ+7l9Aj1bPgBcAHC0Si2A7jF6fTkyw/CEcA+jPx8FN33CPebXA5gW+R3dcxnbokcpy2IiTgFYBHCN4btAP6AyISW/DF1XB5GuAtBAOGnP9dZeUwAFAF4HOFBfO8BOMDp75xNPyrH5y8ANgBYj/BNtJ7Hx7HjczLC3THWA1gX+bmA15B7fjSOEa8jF/wAOBLAB5HjsBHATyOv8xpy6Q9nECciIiIiIluwGxUREREREdmClQ0iIiIiIrIFKxtERERERGQLVjaIiIiIiMgWrGwQEREREZEtWNkgIqKUhBC3CCE+EkKsF0KsE0Icb+O2VgghFtm1fiIiyhyf0wkgIiJ3E0J8CsCFAI6WUo4KIaYCKHA4WURElAXYskFERKnUA+iUUo4CgJSyU0q5TwjxUyHE+0KIjUKIuyOz8EZbJn4rhHhTCPGxEOJYIcSTQohtQohfRJaZK4TYLIRYGmkteUIIUZK4YSHEOUKId4QQa4UQjwshyiKv3yaE2BT57P9kcF8QEZEBrGwQEVEqrwCYJYTYKoS4Uwjx6cjrf5BSHiulPBxAMcKtH1FjUspTAfwJwDMAvgngcADXCCFqIsscBOBuKeWRAPoALIndaKQF5ccAzpJSHg1gNYDvCyGqAXwewGGRz/7Chu9MREQWYGWDiIg0SSkHABwD4AYAHQAeFUJcA+B0IcS7QogNAM4AcFjMx56N/N4A4CMpZUukZWQHgFmR9/ZIKVdG/v4rgJMTNn0CgEMBrBRCrAOwGMAchCsmIwDuFUJcAmDIqu9KRETW4pgNIiJKSUoZBLACwIpI5eJfABwJYJGUco8Q4lYARTEfGY38DsX8Hf0/eu+RiZtJ+F8AWCalvDIxPUKI4wCcCeAKAN9CuLJDREQuw5YNIiLSJIQ4SAixMOalowBsifzdGRlH8QUTq54dGXwOAFcCeDvh/VUAThJCLIiko0QIcWBke1OklC8AuDGSHiIiciG2bBARUSplAH4vhKgEMA6gEeEuVT0Id5PaBeB9E+v9GMBiIcT/AdgG4K7YN6WUHZHuWg8LIQojL/8YQD+AZ4QQRQi3fnzPxLaJiCgDhJSJrdZERET2EkLMBfBcZHA5ERHlKHajIiIiIiIiW7Blg4iIiIiIbMGWDSIiIiIisgUrG0REREREZAtWNoiIiIiIyBasbBARERERkS1Y2SAiIiIiIluwskFERERERLb4/5AaiF8hBOjFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 964.8x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(13.4,5))\n",
    "\n",
    "df.age[(df.income == '>50K\\n')].plot(alpha=.25, color='blue')\n",
    "df2.age[(df2.income == '>50K\\n')].plot(alpha=.45,color='red')\n",
    "\n",
    "plt.ylabel('Age')\n",
    "plt.xlabel('Samples')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what is happening near the mode:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "countx,divisionx = np.histogram(ml2_age, density=True) \n",
    "county,divisiony = np.histogram(fm2_age, density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "val = [(divisionx[i]+divisionx[i+1])/2 for i in range(len(divisionx)-1)]\n",
    "plt.plot(val, countx-county, 'o-') \n",
    "plt.title('Differences in promoting men vs. women')\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Differences',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is still some evidence for our hypothesis!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Remember:\n",
      " We have the following mean values for men, women and the difference:\n",
      "Originally:  39.43354749885268 36.85823043357163 2.5753170652810553\n",
      "For high-income:  44.62578805163614 42.125530110262936 2.5002579413732064\n",
      "After cleaning:  44.317982123920615 41.877028181041844 2.440953942878771\n",
      "\n",
      "The same for the median:\n",
      "38.0 35.0 3.0\n",
      "44.0 41.0 3.0\n",
      "44.0 41.0 3.0\n"
     ]
    }
   ],
   "source": [
    "# The difference between the mean values of male and female populations.\n",
    "print(\"Remember:\\n We have the following mean values for men, women and the difference:\\nOriginally: \", ml_age.mean(), fm_age.mean(),  ml_age.mean()- fm_age.mean()) \n",
    "# The difference between the mean values of male and female populations.\n",
    "print(\"For high-income: \", ml1_age.mean(), fm1_age.mean(), ml1_age.mean()- fm1_age.mean())\n",
    "# The difference between the mean values of male and female populations.\n",
    "print(\"After cleaning: \", ml2_age.mean(), fm2_age.mean(), ml2_age.mean()- fm2_age.mean()) \n",
    "\n",
    "print(\"\\nThe same for the median:\")\n",
    "# The difference between the mean values of male and female populations.\n",
    "print(ml_age.median(), fm_age.median(), ml_age.median()- fm_age.median())\n",
    "# The difference between the mean values of male and female populations.\n",
    "print(ml1_age.median(), fm1_age.median(), ml1_age.median()- fm1_age.median())\n",
    "# The difference between the mean values of male and female populations.\n",
    "print(ml2_age.median(), fm2_age.median(), ml2_age.median()- fm2_age.median())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.5 Measuring asymmetry (optional).\n",
    "\n",
    "**Skewness** is a statistic that measures the asymmetry of set of $n$ data samples $x_i$:\n",
    "\n",
    "$$ g_1 = \\frac{\\frac{1}{n} \\sum_i (x_i - \\mu)^2 }{\\frac{1}{n} \\sum_i (x_i - \\mu)^3 }$$\n",
    "\n",
    "The numerator is the mean squared deviation (or variance) and the denominator the mean cubed deviation.\n",
    "\n",
    "Negative deviation indicates that the distribution \"skews left\" (it extends farther to the left than to the right).\n",
    "\n",
    "**Skewness** can be affected by outliers!!! A simpler alternative is to look at the relationship between mean ($\\mu$) and median ($\\mu_{\\frac{1}{2}}$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The skewness of the male population is: 0.2664443838432819\n",
      "The skewness of the female population is: 0.38633352491285977\n"
     ]
    }
   ],
   "source": [
    "def skewness(x):\n",
    "    res=0\n",
    "    m=x.mean()\n",
    "    s=x.std()\n",
    "    for i in x:\n",
    "        res+=(i-m)*(i-m)*(i-m)\n",
    "    res/=(len(x)*s*s*s)\n",
    "    return res\n",
    "\n",
    "print(\"The skewness of the male population is:\", skewness(ml2_age))\n",
    "print(\"The skewness of the female population is:\", skewness(fm2_age))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.6 Pearson's median skewness coefficient** is a more robust alternative:\n",
    "\n",
    "$$ g_p = \\frac{3(\\mu - \\mu_{\\frac{1}{2}})}{\\sigma} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: Write a function to compute $g_1$ and $g_p$ of the pregnancy length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson's coefficient of the male population is: 0.0952066054901639\n",
      "The Pearson's coefficient of the female population is: 0.2621531209596965\n"
     ]
    }
   ],
   "source": [
    "def pearson(x):\n",
    "    return 3*(x.mean()-x.median())/x.std()\n",
    "\n",
    "print(\"The Pearson's coefficient of the male population is:\", pearson(ml2_age))\n",
    "print(\"The Pearson's coefficient of the female population is:\", pearson(fm2_age))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.6 Relative Risk\n",
    "\n",
    "Let's say that a person is \"early\" promoted if he/she is promoted before the age of 41, \"on time\" if he/she is promoted of age 41, 42, 43 or 44, and \"late\" promoted if he/she is ascended to get income bigger than 50K after being 44 years old. Let us compute the probability of being early, on time and late promoted for men and women:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6601, 15) (1171, 15)\n"
     ]
    }
   ],
   "source": [
    "#ml1 = df[(df.sex == 'Male')&(df.income=='>50K\\n')]\n",
    "\n",
    "ml2 = ml1.drop(ml1.index[(ml1['age'] > df['age'].median() + 35) & (ml1['age'] > df['age'].median() - 15)])\n",
    "fm2 = fm1.drop(fm1.index[(fm1['age'] > df['age'].median() + 35) & (fm1['age'] > df['age'].median() - 15)])\n",
    "\n",
    "print(ml2.shape, fm2.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Men grouped in 3 categories:\n",
      "Young: 38 %.\n",
      "Elder: 48 %.\n",
      "Average age: 14 %.\n"
     ]
    }
   ],
   "source": [
    "print(\"Men grouped in 3 categories:\")\n",
    "print(\"Young:\",int(round(100*len(ml2_age[ml2_age<41])/float(len(ml2_age.index)))),\"%.\")\n",
    "print(\"Elder:\", int(round(100*len(ml2_age[ml2_age >44])/float(len(ml2_age.index)))),\"%.\")\n",
    "print(\"Average age:\", int(round(100*len(ml2_age[(ml2_age>40) & (ml2_age< 45)])/float(len(ml2_age.index)))),\"%.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Women grouped in 3 categories:\n",
      "Young: 48 %.\n",
      "Elder: 37 %.\n",
      "Average age: 15 %.\n"
     ]
    }
   ],
   "source": [
    "print(\"Women grouped in 3 categories:\")\n",
    "print(\"Young:\",int(round(100*len(fm2_age[fm2_age <41])/float(len(fm2_age.index)))),\"%.\")\n",
    "print(\"Elder:\", int(round(100*len(fm2_age[fm2_age >44])/float(len(fm2_age.index)))),\"%.\")\n",
    "print(\"Average age:\", int(round(100*len(fm2_age[(fm2_age>40) & (fm2_age< 45)])/float(len(fm2_age.index)))),\"%.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **relative risk** is the ratio of two probabilities. In order to get the relative risk \\cite{Downey} of early promotion, we need to consider the  fraction of both probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The male mean: 44.317982123920615\n",
      "The female mean: 41.877028181041844\n"
     ]
    }
   ],
   "source": [
    "print(\"The male mean:\", ml2_age.mean())\n",
    "print(\"The female mean:\", fm2_age.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The relative risk of female early promotion is:  21.125440082163816\n"
     ]
    }
   ],
   "source": [
    "ml2_young = len(ml2_age[(ml2_age<41)])/float(len(ml2_age.index))\n",
    "fm2_young  = len(fm2_age[(fm2_age<41)])/float(len(fm2_age.index))\n",
    "print(\"The relative risk of female early promotion is: \", 100*(1-ml2_young/fm2_young))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That means that women are 21% more likely to get high gains before 41 years than men."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The relative risk of male late promotion is:  128.9715708971242\n"
     ]
    }
   ],
   "source": [
    "ml2_elder = len(ml2_age[(ml2_age>44)])/float(len(ml2_age.index))\n",
    "fm2_elder  = len(fm2_age[(fm2_age>44)])/float(len(fm2_age.index))\n",
    "print(\"The relative risk of male late promotion is: \", 100*ml2_elder/fm2_elder)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That means that men are 29% more likely to get high gains after 44 years than women."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussions.\n",
    "\n",
    "After exploring the data, we obtained some apparent effects that seem to support our first assumption:\n",
    "\n",
    "+ **Data description:** The mean age for ascending male professionals is 44 years old while for female professionals it is 41 years.\n",
    "\n",
    "+ **Relative risk:** Female professionals are 21%  more likely to be ascended before 41 years of age, while men are 29% more likely to be ascended being at least 45 years old.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 Continous distributions\n",
    "\n",
    "So far, we have built **empirical distributions** (which represent the distributions of values in a sample), based on observations, but many real problems are well approximated by fitting **continous distributions functions (CDF)**. \n",
    "\n",
    "They are called in this way because the distribution is described by an analytical continous function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.1 The exponential distribution\n",
    "\n",
    "The CDF of the exponential distribution is:\n",
    "\n",
    "$$ CDF(x) = 1 -  \\exp^{- \\lambda x}$$ \n",
    "\n",
    "And its PDF is:\n",
    "\n",
    "$$ PDF(x) = \\lambda \\exp^{- \\lambda x}$$\n",
    "\n",
    "The parameter $\\lambda$ determines the shape of the distribution, the mean of the distribution is $1/\\lambda$ and its variance is $1/\\lambda^2$. The median is $ln(2)/\\lambda$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = 3\n",
    "x=np.arange(0,2.5,0.1)\n",
    "y= 1 - np.exp(-l*x)\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Exponential CDF: $\\lambda$ =%.2f' % l ,fontsize=15)\n",
    "plt.xlabel('x',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "\n",
    "import scipy.stats as stats\n",
    "\n",
    "l = 3\n",
    "x=np.arange(0,2.5,0.1)\n",
    "y= l * np.exp(-l*x)\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Exponential PDF: $\\lambda$ =%.2f' % l, fontsize=15)\n",
    "plt.xlabel('x', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a lot of real world events that can be described with this distribution.\n",
    "* The time until a radioactive particle decays,\n",
    "* The time it takes before your next telephone call,\n",
    "* The time until default (on payment to company debt holders) in reduced form credit risk modeling."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The random variable $X$ of the lifelengths of some batteries is associated with a probability density function of the form:\n",
    "\n",
    "$$ PDF(x) = \\frac{1}{4} \\exp^{- \\frac{x}{4}}$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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curOISAej0GhjZ47rS35OhCfebhcHq4uItCmFRhvrVpDLGWP78tTijZpFJSJZR6GRBhccO5Ct1XXMXaVZVCKSXRQaaXD62L50zc/REJWIZB2FRhoU5EY5e3w/nlmykdqGxrDLERFpMwqNNDn/2IHs3tfAKyu3hl2KiEibUWikycmji+lVmKshKhHJKgqNNMmNRjjnYwN4ftlmaup0RT8RyQ4KjTQ6/5iB7K1v5IXluqKfiGQHhUYaTRrem37d85mlISoRyRIKjTSKRoxPHTOQv63Ywo4P6sIuR0TkiCk00uwzJwymvtG1tSEiWUGhkWbjB3Zn/IDu/PmtyrBLERE5YgqNDPjMxMEsqtzFys17wi5FROSIKDQyYMZxA8mJGH+er60NEenYFBoZUNw1n9OO6sujC9brzLci0qEpNDLksxMHUbWnllcrdFoREem4FBoZcsbYfvQqzNUQlYh0aAqNDMnLiXDBsQN5btlmdtXUh12OiMhhUWhk0GcnDqGuIcYTi3TMhoh0TAqNDDp6UHfG9u/Gw/PWhl2KiMhhUWhkkJlx2YmlLFm/m8WVu8IuR0Sk1RQaGTbjuEEU5EZ48M01YZciItJqCo0M69Ell/OPGcjjCzewZ592iItIx5Lx0DCz6Wa2wswqzOzGJMvHmtkbZlZrZt9stmy1mS02s4VmVp65qtvWZSeWUlPXyOMLtUNcRDqWjIaGmUWB24FzgPHApWY2vlm37cANwE9beJnT3f04dy9LX6XpddyQnowb0J0H/74Wdw+7HBGRlGV6S2MSUOHuq9y9DngYmJHYwd23uPs8IGvHbpp2iC/buJu3tUNcRDqQTIfGIGBdwvPKeFuqHHjOzOab2cyWOpnZTDMrN7Pyqqqqwyw1vS48biBdcqM8+HftEBeRjiPToWFJ2lozPjPV3U8gGN76qplNS9bJ3e929zJ3LyspKTmcOtOuW0EuFxw7kCfe3shu7RAXkQ4i06FRCQxJeD4YSHlvsLtviN9vAR4jGO7qsC6fPJS99Y38qVznoxKRjiHToTEPGG1mw80sD7gEmJXKimZWZGbdmh4DZwNL0lZpBnxscA8mDu3F7+aspjGmHeIi0v5lNDTcvQG4HpgNLAcecfelZnadmV0HYGb9zawS+AbwXTOrNLPuQD/gNTN7G3gTeMrdn81k/enwhanDWLu9hpfe2RJ2KSIih5ST6T/o7k8DTzdruyvh8SaCYavmdgPHpre6zPvkhP4M6FHAfXPe5xPj+4VdjojIQemI8JDlRiNcPnkor1dsY8UmXUNcRNo3hUY7cNmkUvJzItw/5/2wSxEROSiFRjvQqyiPTx8/iMcWrGfHB3VhlyMi0qJDhoaZTYnPVpI0unrqMPbVx3h43rpDdxYRCUkqWxqvAhOanphZxMxeMbPR6Sur8xnbvztTRvbhgTdWU9cQC7scEZGkUgmN5kdxG3Ay0K3ty+ncrp02go279jHrbZ39VkTaJ+3TaEdOG1PC2P7duOvl94jpYD8RaYcUGu2ImfGPp42kYks1L+hgPxFph1I9uO8zZtZ0/YoIwUkGLzKzyc36ubvf2WbVdULnfWwAt85ewZ1/q+AT4/piluwcjyIi4Ug1NL6VpO3bSdocUGgcgZxohJnTRnDz40uZt3oHk4b3DrskEZH9Djk85e6RVtyimSg62100cQh9ivK4828VYZciIvIR2qfRDnXJi3L1lGG8tKKK5Rt3h12OiMh+KYeGBc42s5vN7Pb47WYzO8s08N7mrjxpGEV5UW5/SVsbItJ+pLRPw8yOB/4IjAQaga0Ex2v0ib/GSjO7xN0XpqnOTqdHYS5XTRnGnS+/xw2b9zCmnw6LEZHwpXIakX4E17/YC5wLdHX3ge4+gOAAv/OAOmC2mfVNZ7GdzbWnjKAwN8ptL7wbdikiIkBqw1NfIwiMU9x9trvvP6Oeu9e6+zPAtHif69NTZufUqyiPq6cO4+nFG3XadBFpF1IJjbOBO9y9xT2y7r6TYKrt9DaqS+KuPWUERXk53PbCyrBLERFJKTRGAW+l0G9+vK+0oZ6FeXxh6jCeXrxJM6lEJHSphEYPYFcK/fYA3Y+sHEnmmpOH0y0/h9v+qn0bIhKuVM9ym+rZ8zT1Ng2atjaeXbqJJetTyW8RkfRI9TiN2Wa25WA34Jl0FtrZXXPKCHoW5vLjZ98JuxQR6cRSOU7je2mvQg6pR5dcrj99FD94ajmvvbuVk0cXh12SiHRChwwNd/+emXUhOEZjGLAJ+Ku7b05zbdLMFScN5b7XV/OjZ5bzxMiTiUQ0GigimZXKwX0jgKXAI8CtwO+BFWZ2dpprk2byc6J885NjWLphN08s0tX9RCTzUtmn8RMgRnAAXyHB9cIXAL9OY13SghnHDmLcgO7cOnsFtQ2NYZcjIp1MKqFxEvBdd3/d3fe5+3Lgy0CpmQ1Ib3nSXCRi3HjOWCp37OUPc9eGXY6IdDKphMYAYFWztvcIptf2b/OK5JCmjS7m5FHF/PLFd9lZU3foFURE2kiqU25TPU5DMsDM+LfzxrF7bz0/f16nFxGRzDms4zSAjfH2F5IcryEZMG5Ady6fPJQ/zF2j04uISMboOI0O7BtnjWHW2xv43hNLeejayehaWCKSbikdp5GJQqT1ehbm8S9nH8VNf1nC04s3cd4xmpcgIumV8WuEm9l0M1thZhVmdmOS5WPN7A0zqzWzb7Zm3c7oskmljBvQnf98ejl76zQFV0TSK6OhYWZR4HbgHGA8cKmZjW/WbTtwA/DTw1i304lGjFvOH8/6nXu542+6nriIpFemtzQmARXuvip+BcCHgRmJHdx9i7vPA+pbu25ndeKIPlx43EDuevk93t2sK/yJSPpkOjQGAesSnlfG29p0XTObaWblZlZeVVV1WIV2NN/91HiK8nP4zmOLicU0Q1pE0iPToZFses+RXKsj6brufre7l7l7WUlJScrFdWTFXfP5zrnjmLd6Bw/PW3foFUREDkOmQ6MSGJLwfDCQ6pn3jmTdTuGiiYOZPKI3P3pmOVt27wu7HBHJQpkOjXnAaDMbbmZ5wCXArAys2ymYGT/89MeorY/xvSeXhV2OiGShjIaGuzcA1wOzgeXAI+6+1MyuM7PrAMysv5lVAt8AvmtmlWbWvaV1M1l/RzCypCvXnzGKpxZt5Lmlm8IuR0SyjLln907TsrIyLy8vD7uMjKpriDHj9tep2rOP5/75VHoX5YVdkoh0IGY2393Lki3L+MF9kn55ORF+fvGx7Npbz01/WRJ2OSKSRRQaWWrcgO780yfG8NTijTzxtuYLiEjbUGhksS9PG8FxQ3py0+NLNJtKRNqEQiOL5UQj/OziY9lb18iNjy4m2/dfiUj6KTSy3MiSrvzrOWN58Z0t3D9nddjliEgHp9DoBK6aMowzx/blR0+/w5L1u8IuR0Q6MIVGJ2Bm3HrRsfQqyuVrDy3gg9qGsEsSkQ5KodFJ9C7K47ZLjmfNtg+4+XEdEykih0eh0YlMHtGH688YzZ/fquTRtyrDLkdEOiCFRidzwxmjOHF4b77z2GKWbdgddjki0sEoNDqZnGiEX112Aj265PLlP5Szs6Yu7JJEpANRaHRCJd3yufPyiWzatY8bHl5Ioy7aJCIpUmh0UieU9uKWCybwysoqfvHXlWGXIyIdhEKjE7tsUikXlw3mly9W8NSijWGXIyIdgEKjEzMzvj/jaCYO7cU3HlnIwnU7wy5JRNo5hUYnV5Ab5e4rJtK3ez5f+l05lTtqwi5JRNoxhYbQp2s+9171cWrrG7nm/nL27KsPuyQRaacUGgLA6H7duOPyE6ioquarDy6gvjEWdkki0g4pNGS/U0aX8MMLj+aVlVV8609vE9NUXBFpJifsAqR9uWRSKVura/npcyvpVZTHzZ8aj5mFXZaItBMKDTnAV08fxbYP6rjv9dUUd83nq6ePCrskEWknFBpyADPjpvPGs7Omnltnr6B7l1yumDw07LJEpB1QaEhSkYjxk88ew+699dz0lyXkRIxLJ5WGXZaIhEw7wqVFudEId1x+AqcdVcK/PrqYR+atC7skEQmZQkMOKj8nyl2XT+SU0cV8+9FF/N98XYdDpDNTaMghFeRGuefKMqaOLOZb//c2D725NuySRCQkCg1JSVNwTBsdDFXd88qqsEsSkRAoNCRlXfKC4DjvYwP44dPL+dlzK3DXAYAinYlmT0mr5OVE+J9Lj6coP8ovX6xg9956bj5/AtGIDgAU6QwUGtJq0Yjx488cQ48uudzz6vts2r2PX3zueLrkRcMuTUTSTMNTcljMjH87bzw3f2o8zy3bzKX3zGVrdW3YZYlImmU8NMxsupmtMLMKM7sxyXIzs/+JL19kZickLFttZovNbKGZlWe2cknmiycP567LJ/LOpt38wx1zqNhSHXZJIpJGGQ0NM4sCtwPnAOOBS81sfLNu5wCj47eZwJ3Nlp/u7se5e1m665XUfHJCfx6eeRI1dQ18+vbXefGdzWGXJCJpkuktjUlAhbuvcvc64GFgRrM+M4AHPDAX6GlmAzJcp7TScUN68vj1JzO0uJBrflfO7S9VaGaVSBbKdGgMAhLPRVEZb0u1jwPPmdl8M5vZ0h8xs5lmVm5m5VVVVW1QtqRiUM8u/OnLUzj/mIHcOnsF1z+4gOrahrDLEpE2lOnQSDYvs/nP0YP1meruJxAMYX3VzKYl+yPufre7l7l7WUlJyeFXK63WJS/KbZccx3fOHcszSzZy/i9fY8n6XWGXJSJtJNOhUQkMSXg+GNiQah93b7rfAjxGMNwl7YyZMXPaSB66djI1dQ38wx1zeOCN1RquEskCmQ6NecBoMxtuZnnAJcCsZn1mAVfGZ1FNBna5+0YzKzKzbgBmVgScDSzJZPHSOieO6MMzX5/G1FF9uPnxpVz3h/nsqqkPuywROQIZDQ13bwCuB2YDy4FH3H2pmV1nZtfFuz0NrAIqgHuAr8Tb+wGvmdnbwJvAU+7+bCbrl9brXZTHb6/6OP927jheWL6Fc//nVea8tzXsskTkMFm2DxmUlZV5ebkO6WgPFqzdwTceeZv3t37AlScN5dvTx1KUr5MSiLQ3Zja/pcMadES4ZMzxpb14+oZT+OLU4fx+7hqm3/YKc1dtC7ssEWkFhYZkVJe8KDefP54/zjyJiBmX3D2Xf398CXv2aV+HSEeg0JBQTBrem2e+fgpXTxnGA3PXcObPXubxhes1w0qknVNoSGgK83K45YIJ/OUrU+nfo4CvP7yQy+75OxVb9oRdmoi0QKEhoTt2SE8e+8pUfnDh0SzdsItzbnuVHz2znN0ashJpdxQa0i5EI8blk4fy4jdP48LjBvHrl1dx6k9e4r7X36euIRZ2eSISp9CQdqW4az63XnQsT37tZMYP7M73nljGJ37+Mk8u2qD9HSLtgEJD2qWjB/XgD9ecyP1f+DiFeVGuf3ABM25/nReWb1Z4iIRIoSHtlplx2lF9eeqGU7j1s8ewo6aOa35XzgW/ep3nlyk8RMKgI8Klw6hvjPHYgvXc/lIFa7bVMGFgd64/fRRnT+hPNJLs5MgicjgOdkS4QkM6nIbGGH9ZuIFfvfguq7fVUNq7kC9OHcZFZUN0WhKRNqDQUGhkpcaY89zSTdzz6ireWruT7gU5fH7yUK48aSgDenQJuzyRDkuhodDIevPX7OA3r65i9tJNAJw5rh+fP7GUaaNLiGjoSqRVDhYa2paXrDBxaC8mDp3Iuu01PPTmWh4pX8fzyzYzuFcXLjuxlM+cMJh+3QvCLlOkw9OWhmSluoYYzy3bxP/OXcsbq7YRMZg6qphPHz+IT07or30fIgeh4SmFRqe2qqqaxxas57EF66ncsZfCvCifnNCfTx8/iKmjijXzSqQZhYZCQ4BYzClfs4PHFlTy5KKN7NnXQJ+iPM4a349PHt2fKSP7kJ8TDbtMkdApNBQa0sy++kb+tmILTy/exIvvbKG6toFu+TmcMa4v0yf0Z9qYEg1hSaelHeEizRTkRpl+9ACmHz2A2oZG5lRs49klm3hu2SYeX7iB3Kjx8WG9Oe2oEk4d05cx/bpipmEsEW1piCRoaIwxb/UOXlqxhZdXVLFic3BtjwE9Cjh1TAmnjC7hxBG9Ke6aH3KlIumj4SmFhhymjbv28vKKKl5eWcVr725lT20DAKP7dmXyiD5MHtFHISJZR6Gh0JA2UN8YY8n6XcxdtZ25q7ZRvno7H9Q1AjCipIgTSntx3JCeHF/ak6P6dSMnqvOBSsek0FBoSBokhsj8NdtZsHYn2z6oA6BLbpSPDe7B8aU9OX5ITyYM7MHgXl20X0Q6BO0IF0mD3GiE40t7cXxpL2Ak7s667XtZsG4HC9buZMG6ndz72vvUNwY/zLoV5DB+QHfGD+y+/350327k5WiLRDoOhYZIGzEzSvsUUtqnkBnHDQKCqb3LN+5m2cbdLNsQ3D/85jr21gfDWjkRY3hxEaP6dmVU366MLAnuR5QUUZin/z2l/dG/SpE0KsiNJmyNBBpjzpptH+wPkne3VLNi0x6eW7aZxtiHw8WDenZhZN+ujCrpytA+hZT2LmRI70IG9+pCQa4OQpRwKDREMiwaMUaUdGVESVc+dczA/e21DY2s2VZDxZZq3ttSTUVVNRVbqpn3/vb9WyZN+ncvCLZqege3QT27MKBnAQN6dGFAjwKFiqSNQkOkncjPiTKmXzfG9Ov2kXZ3Z2t1HWu317Buew1rttXsf/zau1vZtHvfAa/VqzCX/vEA+fDWhZJu+RR3zae4Wx69C/M0w0taTaEh0s6ZGSXd8inpls/Eob0OWL6vvpGNu/axcddeNu3at//xxp3B44XrdrI9Pqvro68LvQvz9odIcdf8hFsevYvy6FmYS48uTfe55CpkOj2FhkgHV5AbZXhxEcOLi1rss6++kU279lFVXcvWPbVsra6lqrqOrQnPF6zdydbqWmrqGlt8na75OfTokkuvolx6dsmjR2EuPbvk0rMwl+4FuXQtyKFrfg7dCnIoysuha0EO3fI/bNdMsY4v46FhZtOB24Ao8Bt3/69myy2+/FygBrja3d9KZV0RSa4gN8qw4iKGHSRYmtTUNbB1Tx0799axs6aenXvr2VkTf1xTz869deyKt2/cuHd/n8Sd+C3Jy4nQLT9nf4gU5edQmBelS278lpdw30J7YV6UgoT2vGiEvJz4LRrRsTBpltHQMLMocDtwFlAJzDOzWe6+LKHbOcDo+O1E4E7gxBTXFZEjVJiXQ2mfHEopTHkdd2dvfSPV+xrYU9tA9b4Gqmsb2BO/r95XHzxPWNbUd/sHdeyta2RvfeOH9/WNHO5xx3k5EfITgiQ/56OhErRFP1we/bBfTjRCTtTIjUSIRozcqAVtEQtu0Qi5USMaCe5zDtIvuDdy44+jESNiwX00YphBNP48EjGiFiyPRD5sb48BmOktjUlAhbuvAjCzh4EZQOIX/wzgAQ8OVZ9rZj3NbAAwLIV1RSQEZkZhXg6FeTn0bYPXc3dqG2L7Q6SmrpF99R8GS+LzuoZYcGuMUVvfSG1j7MO2hhi1Ccub2nbW1AXtjR/t09AYoz7mNDTGSGHDKSOiTYESIQgdi4dMPIQixkcCKWIQiRjFRfk8ct1JbV5PpkNjELAu4XklwdbEofoMSnFdAMxsJjAToLS09MgqFpGMMzMKcoNhqAN3/WdGLOY0xJyGWCy4bwzCpOlxfSxGY8ypb4wFy2JN90FbsCxob4yv0+hOLObEnP2PG2NOzINbY4z4fbwtFqzT1N70fP+9s/81Gt1xZ//jbmm6HkymQyPZtlbzPG+pTyrrBo3udwN3Q3DuqdYUKCICwa/1vIiRh3beJ8p0aFQCQxKeDwY2pNgnL4V1RUQkjTIdofOA0WY23MzygEuAWc36zAKutMBkYJe7b0xxXRERSaOMbmm4e4OZXQ/MJpg2e6+7LzWz6+LL7wKeJphuW0Ew5fYLB1s3k/WLiHR2up6GiIh8xMGup6E9PCIikjKFhoiIpEyhISIiKVNoiIhIyrJ+R7iZVQFrDnP1YmBrG5bTEeg9dw56z53D4b7noe5ekmxB1ofGkTCz8pZmEGQrvefOQe+5c0jHe9bwlIiIpEyhISIiKVNoHNzdYRcQAr3nzkHvuXNo8/esfRoiIpIybWmIiEjKFBoiIpIyhUYSZjbdzFaYWYWZ3Rh2PZliZqvNbLGZLTSzrDzLo5nda2ZbzGxJQltvM3vezN6N34d1sbi0aOE932Jm6+Of9UIzOzfMGtuamQ0xs5fMbLmZLTWzr8fbs/azPsh7btPPWvs0mjGzKLASOIvgglDzgEvdPeuvRW5mq4Eyd8/aA6DMbBpQTXAd+qPjbT8Btrv7f8V/JPRy92+HWWdbauE93wJUu/tPw6wtXcxsADDA3d8ys27AfOBC4Gqy9LM+yHu+mDb8rLWlcaBJQIW7r3L3OuBhYEbINUkbcfdXgO3NmmcAv4s//h3B/2hZo4X3nNXcfaO7vxV/vAdYDgwiiz/rg7znNqXQONAgYF3C80rS8B++nXLgOTObb2Yzwy4mg/rFrw5J/L5vyPVkyvVmtig+fJU1wzTNmdkw4Hjg73SSz7rZe4Y2/KwVGgeyJG2dZQxvqrufAJwDfDU+rCHZ6U5gJHAcsBH4WajVpImZdQX+DPyTu+8Ou55MSPKe2/SzVmgcqBIYkvB8MLAhpFoyyt03xO+3AI8RDNV1Bpvj48FN48JbQq4n7dx9s7s3unsMuIcs/KzNLJfgy/N/3f3ReHNWf9bJ3nNbf9YKjQPNA0ab2XAzywMuAWaFXFPamVlRfOcZZlYEnA0sOfhaWWMWcFX88VXA4yHWkhFNX5xxnybLPmszM+C3wHJ3/3nCoqz9rFt6z239WWv2VBLxKWm/AKLAve7+w3ArSj8zG0GwdQGQAzyYje/bzB4CTiM4ZfRm4N+BvwCPAKXAWuAid8+aHcctvOfTCIYrHFgNfLlprD8bmNnJwKvAYiAWb/4OwRh/Vn7WB3nPl9KGn7VCQ0REUqbhKRERSZlCQ0REUqbQEBGRlCk0REQkZQoNERFJmUJDRERSptAQEZGUKTRERCRlCg2RDDGznmZWaWYPNGufZWYrzawwrNpEUqXQEMkQd98JXANcYWYXApjZF4DzgKvdvSa86kRSo9OIiGSYmf2a4OI/04GXgF9ny9XjJPspNEQyLH69g0XAQKACmOjuteFWJZIaDU+JZJi7VwNPAvnAbxUY0pFoS0Mkw8ysDHiD4BTWQ4EJ7r4p3KpEUqPQEMkgMysA3gJWARcDbxNcNOeCUAsTSZGGp0Qy6wdAf+Da+Gypq4DzzOzqUKsSSZG2NEQyxMymAq8AV7j7gwnttwLXAke7e2VY9YmkQqEhIiIp0/CUiIikTKEhIiIpU2iIiEjKFBoiIpIyhYaIiKRMoSEiIilTaIiISMoUGiIikrL/D04/9I8UYQ0LAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = 0.25\n",
    "x=np.arange(0,25,0.1)\n",
    "y= l * np.exp(-l*x)\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Exponential: $\\lambda$ =%.2f' % l ,fontsize=15)\n",
    "plt.xlabel('x',fontsize=15)\n",
    "plt.ylabel('PDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.2 The normal distribution\n",
    "\n",
    "The **normal, or Gaussian distribution** is the most used one because it describes a lot of phenomena and because it is amenable for analysis. \n",
    "\n",
    "Its CDF has no closed-form expression and its more common representation is the PDF:\n",
    "\n",
    "$$ PDF(x) = \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\exp \\left(-\\frac{(x-\\mu)^2}{2 \\sigma^2} \\right)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u=6 # mean\n",
    "s=2 # standard deviation\n",
    "x=np.arange(0,15,0.1)\n",
    "y=(1/(np.sqrt(2*np.pi*s*s)))*np.exp(-(((x-u)**2)/(2*s*s)))\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Gaussian PDF: $\\mu$=%.1f, $\\sigma$=%.1f' % (u,s),fontsize=15)\n",
    "plt.xlabel('x',fontsize=15)\n",
    "plt.ylabel('Probability density',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Examples:\n",
    "    * Measures of size of living tissue (length, height, skin area, weight);\n",
    "    * The length of inert appendages (hair, claws, nails, teeth) of biological specimens, in the direction of growth; presumably the thickness of tree bark also falls under this category;\n",
    "    * Certain physiological measurements, such as blood pressure of adult humans.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.5 Central Limit Theorem\n",
    "\n",
    "The normal distribution is also important, because it is involved in the Central Limit Theorem:\n",
    "\n",
    "> Take the mean of $n$ random samples from ANY arbitrary distribution with a $well$ $defined$ standard deviation $\\sigma$ and mean $\\mu$. As $n$ gets bigger the **distribution of the sample mean** will always converge to a Gaussian (normal) distribution with mean $\\mu$ and standard deviation $\\frac{\\sigma}{\\sqrt{n}}$.\n",
    "\n",
    "Colloquially speaking, the theorem states the distribution of an average tends to be normal, even when the distribution from which the average is computed is decidedly non-normal. This explains the ubiquity of the Gaussian distribution in science and statistics. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: Uniform Distribution\n",
    "\n",
    "The uniform distribution is obviously non-normal.  Let's call it the $parent$ $distribution$.\n",
    "\n",
    "To compute an average, two samples are drawn ($n=2$), at random, from the parent distribution and averaged. Then another sample of two is drawn and another value of the average computed.  This process is repeated, over and over, and averages of two are computed.  \n",
    "\n",
    "Repeatedly taking more elements ($n = 3,4...$) from the parent distribution, and computing the averages, produces a normal probability density."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 4, sharey=True, squeeze=True, figsize=(14, 5))\n",
    "x = np.linspace(0, 1, 100)\n",
    "for i in range(4):\n",
    "    f = np.mean(np.random.random((10000, i+1)), 1)\n",
    "    m, s = np.mean(f), np.std(f, ddof=1)\n",
    "    fn = (1/(s*np.sqrt(2*np.pi)))*np.exp(-(x-m)**2/(2*s**2))  # normal pdf            \n",
    "    ax[i].hist(f, 40, density=True, color=[0, 0.2, .8, .6]) \n",
    "    ax[i].set_title('n=%d' %(i+1))\n",
    "    ax[i].plot(x, fn, color=[1, 0, 0, .6], linewidth=5)\n",
    "plt.suptitle('Demonstration of the central limit theorem for a uniform distribution', y=1.05)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.6 Kernel density estimates\n",
    "\n",
    "In some instances, we may not be interested in the parameters of a particular distribution of data, but just a **continous representation** of the data at hand. In this case, we can estimate the distribution non-parametrically (i.e. making no assumptions about the form of the underlying distribution) using kernel density estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa3ba04cd60>]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats.distributions import norm\n",
    "\n",
    "# Some random data\n",
    "y = np.random.random(15) * 10\n",
    "x = np.linspace(0, 10, 100)\n",
    "\n",
    "x1 = np.random.normal(-1, 2, 15) # parameters: (loc=0.0, scale=1.0, size=None)\n",
    "x2 = np.random.normal(6, 3, 10)\n",
    "y = np.r_[x1, x2] # r_ Translates slice objects to concatenation along the first axis.\n",
    "x = np.linspace(min(y), max(y), 100)\n",
    "\n",
    "\n",
    "# Smoothing parameter\n",
    "s = 0.4\n",
    "\n",
    "# Calculate the kernels\n",
    "kernels = np.transpose([norm.pdf(x, yi, s) for yi in y])\n",
    "\n",
    "plt.plot(x, kernels, 'k:')\n",
    "plt.plot(x, kernels.sum(1), 'r')\n",
    "plt.plot(y, np.zeros(len(y)), 'go', ms=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa39c96f850>]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import kde\n",
    "\n",
    "x1 = np.random.normal(-1, 0.5, 15) # parameters: (loc=0.0, scale=1.0, size=None)\n",
    "x2 = np.random.normal(6, 1, 10)\n",
    "y = np.r_[x1, x2] # r_ Translates slice objects to concatenation along the first axis.\n",
    "x = np.linspace(min(y), max(y), 100)\n",
    "\n",
    "s = 0.4 # Smoothing parameter\n",
    "\n",
    "kernels = np.transpose([norm.pdf(x, yi, s) for yi in y]) # Calculate the kernels\n",
    "density = kde.gaussian_kde(y)\n",
    "\n",
    "plt.plot(x, kernels, 'k:')\n",
    "plt.plot(x, kernels.sum(1), 'r')\n",
    "plt.plot(y, np.zeros(len(y)), 'bo', ms=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa39c4f20d0>]"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xgrid = np.linspace(x.min(), x.max(), 200)\n",
    "plt.hist(y, bins=28, density=True)\n",
    "plt.plot(xgrid, density(xgrid), 'r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SciPy implements a Gaussian KDE that automatically chooses an appropriate bandwidth. Let's create a bi-modal distribution of data that is not easily summarized by a parametric distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a bi-modal distribution with a mixture of Normals.\n",
    "x1 = np.random.normal(-1, 2, 15) # parameters: (loc=0.0, scale=1.0, size=None)\n",
    "x2 = np.random.normal(6, 3, 10)\n",
    "\n",
    "# Append by row\n",
    "x = np.r_[x1, x2] # r_ Translates slice objects to concatenation along the first axis.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.28073777, 0.16844266, 0.16844266, 0.11229511, 0.05614755,\n",
       "        0.05614755, 0.05614755, 0.        , 0.11229511, 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.05614755, 0.16844266,\n",
       "        0.        , 0.05614755, 0.11229511]),\n",
       " array([-4.53230805, -3.81989946, -3.10749086, -2.39508227, -1.68267367,\n",
       "        -0.97026508, -0.25785648,  0.45455211,  1.16696071,  1.87936931,\n",
       "         2.5917779 ,  3.3041865 ,  4.01659509,  4.72900369,  5.44141228,\n",
       "         6.15382088,  6.86622947,  7.57863807,  8.29104667]),\n",
       " <BarContainer object of 18 artists>)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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b++/1fcC/TEjI0/+ZPJvkN/tN7wCeGWNJo/oecFOSV/ffR+9gg/6YfMWc0Tfu74FfAr7W/63k8ao6MN6Sljcht8ZYzs3AB4CnkjzRb/vzqjo2vpKuKH8MfLF/gnCa/u1WJkFVfSPJl4Fv0lti/RYbdDsEb4EgSY274pduJKl1Br0kNc6gl6TGGfSS1DiDXpIaZ9BLUuMMeklq3P8A8cM2mi39kPYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x, bins=18, density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa39d117310>]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "density = kde.gaussian_kde(x)\n",
    "xgrid = np.linspace(x.min(), x.max(), 200)\n",
    "plt.hist(x, bins=18, density=True)\n",
    "plt.plot(xgrid, density(xgrid), 'r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## 4 Estimation\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.normal(0.0, 1.0, 10000)\n",
    "a = plt.hist(x, 50, density=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**Definition:** *Estimation* is the process of inferring the parameters (e.g. mean) of a distribution from a statistic of samples drown from a population.\n",
    "\n",
    "For example: What is the estimated mean $\\hat{\\mu}$ of the following normal data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use our definition of empirical mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The empirical mean of the sample is  0.0059327769746846054\n"
     ]
    }
   ],
   "source": [
    "print('The empirical mean of the sample is ', x.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Sample mean\n",
    "\n",
    "+ The process is called **estimation** and the statistic we used **estimator**.\n",
    "\n",
    "+ The median is also an estimator (more robust to outliers). \n",
    "\n",
    "+ \"Is median better than sample mean?\" is a question with at least two different answers. We can use two different objectives to answer this question: the minimization of error or the maximization to get the right answer. \n",
    "\n",
    "+ If there are no outliers, we can use the **sample mean** to minimize **mean squared error** (where $m$ is the number of times you play the estimation game, not the size of the sample!):\n",
    "\n",
    "$$ MSE = \\frac{1}{m} \\sum(\\hat{\\mu} - \\mu)^2$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  0.0009126820832984471\n"
     ]
    }
   ],
   "source": [
    "NTs=200\n",
    "mu=0.0\n",
    "var=1.0\n",
    "err = 0.0\n",
    "NPs=1000\n",
    "for i in range(NTs):\n",
    "    x = np.random.normal(mu, var, NPs)\n",
    "    err += (x.mean()-mu)**2\n",
    "\n",
    "print('MSE: ', err/NTs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Variance\n",
    "\n",
    "We can also estimate the variance with:\n",
    "\n",
    "$$ \\hat{\\sigma}^2 = \\frac{1}{n} \\sum_i (x_i - \\mu)^2 $$\n",
    "\n",
    "This estimator works for large samples, but it is biased for small samples. We can use this one:\n",
    "\n",
    "$$ \\hat{\\sigma}^2_{n-1} = \\frac{1}{n-1} \\sum_i (x_i - \\mu)^2 $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 Other concepts: Standard scores\n",
    "\n",
    "$$ z_i = \\frac{x_i - \\mu}{\\sigma}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This measure is dimensionless and its distribution has mean 0 and variance 1.\n",
    "\n",
    "It inherits the \"shape\" of $X$: if it is normally distributed, so is $Z$. If $X$ is skewed, so is $Z$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 Covariance\n",
    "\n",
    "**Covariance** is a measure of the tendency of two variables to vary together. \n",
    "\n",
    "If we have two series $X$ and $Y$ with $X=\\{x_i\\}$ and $Y=\\{y_i\\}$, and they vary together, their deviations $x_i - \\mu_X$ and $y_i - \\mu_Y$ tend to have the same sign.\n",
    "\n",
    "If we multiply them together, the product is positive, when the deviations have the same sign, and negative, when they have the opposite sign. So adding up the products gives a measure of the tendency to vary together.\n",
    "\n",
    "Covariance is the mean of the products:\n",
    "\n",
    "$$ Cov(X,Y) = \\frac{1}{n} \\sum_{i=1}^n (x_i - \\mu_X)*(y_i - \\mu_Y), $$\n",
    "\n",
    "where $n$ is the length of the two series.\n",
    "\n",
    "It is a measure that is difficult to interpret."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cov(X, X) = 18.89\n",
      "Var(X) = 18.89\n",
      "Cov(X, Y) = 0.18\n"
     ]
    }
   ],
   "source": [
    "def Cov(X, Y):\n",
    "    def _get_dvis(V):\n",
    "        return [v - np.mean(V) for v in V]\n",
    "    dxis = _get_dvis(X)\n",
    "    dyis = _get_dvis(Y)\n",
    "    return np.sum([x * y for x, y in zip(dxis, dyis)])/len(X)\n",
    "\n",
    "\n",
    "X = [5, -1, 3.3, 2.7, 12.2]\n",
    "X= np.array(X)\n",
    "Y = [10, 12, 8, 9, 11]\n",
    "\n",
    "print(\"Cov(X, X) = %.2f\" % Cov(X, X))\n",
    "print(\"Var(X) = %.2f\" % np.var(X))\n",
    "\n",
    "print(\"Cov(X, Y) = %.2f\" % Cov(X, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us create some examples of positive and negative correlations like those showing the relations of stock market with respect to the economic growth or the gasoline prices with respect to the world oil production:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "MAXN=100\n",
    "\n",
    "MAXN=40\n",
    "X=np.array([[1,9],[3, 2], [5,3],[5.5,4],[6,4],[6.5,4],[7,3.5],[7.5,3.8],[8,4],\n",
    "            [8.5,4],[9,4.5],[9.5,7],[10,9],[10.5,11],[11,11.5],[11.5,12],[12,12],[12.5,12],[13,10]])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(1,2,1)\n",
    "plt.scatter(X[:,0],X[:,1],color='b',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('Economic growth(T)',fontsize=15)\n",
    "plt.ylabel('Stock market returns(T)',fontsize=15)\n",
    "plt.gcf().set_size_inches((20,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SpKoqn5td3pvn+RRT3h8GXAlcAGzOzKtqqU6SJA21SiMqEXEc8G3gz4FrgHPLxw3At8v1kiRJPVV1ROXtwCTw+Mz82fTCiDgY2AGMA85DKEmSeqrqOSr3B948M6QAZOb1wJuAB/S6MEmSpKpB5ZvAmjnWHQZc2ptyJEmS9qp66GcT8M8RcT3w0cy8OSIOBJ4IvAR4Rl0FSpKk4VU1qHwMOAh4L0AZWA4u190EfCQibm2cmYf2sEZJkjSkqgaV/8u+U+ZLkiTVrurMtK+quQ5JkqTbcGZaSZLUWgYVSZLUWgYVSZLUWgYVSZLUWgYVSZLUWl0FlYg4MSJeERHbI+LIctkjIuIe9ZQnSZKGWaXLkyPi7sDHgbXAd4GjgW3A5cAzKSZ9G6unREmSNKyqjqiMU8xEe//yI2as+3fg+B7XJUmSVHlm2hOAUzLzOxFxQMe6K4DDe1uWJElSd+eo/GKO5YcAN/agFkmSpH1UDSr/CWzqGE2ZvvfPnwH/0dOqJEmSqH7o58XAF4CLgY9QhJRnR8QxwDHAw+opT5IkDbNKIyqZeTHFFT8TwKkUh4H+EPg+8NDM/FZdBUqSpOFVdUSFzLwMeHqNtUiSJO3DmWklSVJrVQ4qEfHHEfHeiDgvIr7c+VFnkZKkfU1Nwfr1sGYNrFhRPK5fXyyXBknVmWlfBfwN8DXgm8DPa6xJkjSHPXtg0ybYtm3f5TfdBGecUXxs2ADj47Cs8sF9qb2qfhs/C3h9Zr6sF52WlzlPAD/IzHW9eE1JGgazhZRO27ZBBGzZ0p+apDpVPfRzJ+DcHvb7POCSHr6eJA28qamFQ8q0rVs9DKTBUDWovI9iGv39FhFHAI8D3tGL15OkYdHtCMnWrfXUIfVT1UM/5wJviIhDgM8AuzobZOa/VXyttwIvohilkSRVtGNHve2lNqoaVN5fPh4FnDLL+gQ6b1Z4GxGxDrg6Mycj4nfnaXcacBrAkUceWbFESRpsu3d3137XrlrKkPqqalA5ukf9HQecFBGPBZYDd46If8nMp81slJnbge0Ao6OjeduXkaThs3JlcXVPVatW1VaK1DdVp9D/3kIfFV/npZl5RGYeBTwZ+I/OkCJJmt26Lq+R7La91EZzBpWIOGjm5wt99KdcSRpeGzd2135srJ46pH6ab0Tluoh4SPn59cB1C3x0JTM/5xwqklTdyEgxmVsVY2NFe2mpm+8clT8DLpvxueeKSFLDxseLydzmu/R4bAw2b+5fTVKdIrPd+WN0dDQnJiaaLkOSWmVqqggrO3YUV/esWlWck+JIipaiiJjMzNHZ1nknCElagkZG4PTTm65Cqt+cQSUivkIXh3sy8yELt5IkSapuvhGVb+B5KZIkqUFzBpXMPLWPdUiSJN1G1+eolPf7uQvwk8z8ce9LkiRJKlS9ezIR8aSIuAS4CrgUuDoiLomIP6mtOkmSNNQqjahExFOA9wCfBF5HEVbuDjwJeF9EHJCZ76utSkmSNJSqHvp5ObA9MzvnRPyniNgG/DVgUJEkST1V9dDPrwAfmmPdh8r1kiRJPVU1qFwFzDpjXLn8qt6UI0mStFfVQz/vAl4VEQcAZ1MEk0OBP6E47PO6esqTJEnDrGpQ+Vvg9sBLgFfPWH4j8KZyvSRJUk9VCiqZ+Uvg5RHxJuAY4DDgSuDizPxpjfVJkqQh1tWEb2Uo+c+aapEkSdpHpZNpI+KPIuJZM54fHRFfjIhdEfGhiFhVW4WSJGloVb3q56+BO894Pg4cArweGAFe2+O6JEmSKh/6uTfwdYCIWAn8PvDEzPxERFxOEVieU0+JkiRpWFW+1w+Q5eMjgV8A/14+vwJY3cuiJEmSoHpQ+Rrw1Ii4I7Ae+Gxm3lyuOxK4uo7iJEnScKt66OdlwL8CpwDXUxz6mfYE4ILeliVJklR9HpUvRMSRwH2ByzJz14zV7wS+U0NtkiRpyFWeRyUzrwMmZ1n+bz2tSJIkqVQ5qETEnYCTKUZVlneuz8wX9bAuSZKkakElIu4D/BdwEHBHYCdw1/LrfwrsBgwqkiSpp6pe9fMWYAK4OxDAY4EVwNMoTq59Ui3VSZKkoVb10M9DKC5Lnr4k+Q6Z+QvgvRFxCPA24Nga6pMkSUOs6ojKcuDa8i7KPwHuMWPdxcADe12YJElS1aDyLeBe5edfBTZExPKIuD3wLOCHdRQnSZKGW9VDP+8DHgT8M/AK4NPAtcAvy9c4tYbaJEnSkKs64ds/zvj8SxFxDHAixSGh/8jMi2uqT5KkW01NwZYtsGMH7N4NK1fCunWwcSOMjDRdneoQmblwqwaNjo7mxMRE02VIkhq0Zw9s2gTbts3dZsMGGB+HZZVnCFNbRMRkZo7Otm7etzMijgZuzMwfzVi2saPZ9Zn5T/tfpiRJs1sopECxPqIYcdHgmHNEJSKOBf4TOCkzP1EuOwC4paNpAidm5jkLdhaxHDgPOJAiJJ2dma+c72scUZGk4TY1BWvXVm8/OelhoKVmvhGV+a762QR8cjqkdBjNzNtl5u2AbcCzK9ZyM/CozHwgxcm5J0TEwyp+rSRpCHU7QrJ1az11qBnzBZXfAc6q8BrnAA+v0lkWri+f3r78aPdJMpKkRu3YUW97tdt8QWU18L2ZC8rZaP8K+P6MxT8u21YSEQdExIXA1cBnMvOCWdqcFhETETGxc+fOqi8tSRpAu3d3137XrlrKUEPmCyrXAXfrXJiZb87MmenhkLJtJZn5i8x8EHAE8JDyUufONtszczQzR1evrpyBJEkDaOXK7tqvWlVLGWrIfEFlEnh8hdd4fNm2K5m5C/gccEK3XytJGh7r1tXbXu02X1DZCpwaEU+fq0FEPA14BlDpVKeIWB0Rq8rPVwCPBi6tXK0kaehs7JwUYwFjY/XUoWbMOY9KZn40IsaBd0fEcyhOmv0+xcmvRwC/DzwUeFtmfqxif4eVr3cARUj6QGZ62pMkaU4jI8VkbgvNowJFSPHS5MEy74RvmfmCiPgc8DyKk2gPLFfdDJwPPDEzP161s8y8CHjw4kqVJA2r8fFiMrf5Lj0eG4PNm/tXk/qj8hT65SjI3YAArimvAKqdE75JkqZNTRVhZceO4uqeVauKc1IcSVnaFj2F/kxlMLm6Z1VJktSlkRE4/fSmq1A/zXcyrSRJUqMMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkqbUMKpIkLWBqCtavhzVrYMWK4nH9+mL5IPfdBpGZTdcwr9HR0ZyYmGi6DEnSENqzBzZtgm3b5m6zYQOMj8OyZYPTd79FxGRmjs62rq8jKhFxz4j4bERcEhHfiIjn9bN/SZK6sVBQgGL9c587WH23SV9HVCLiMOCwzJyKiDsBk8ATMvObc32NIyqSpCZMTcHatdXbT07CyMjS77sJrRlRycwrM3Oq/Pw64BLg8H7WIElSFVu2dNd+69bB6LttGjuZNiKOAh4MXNBUDZIkzWXHjnrbt7XvtmkkqETEwcCHgOdn5rWzrD8tIiYiYmLnzp39L1CSNPR27+6u/a5dg9F32/Q9qETE7SlCynsy88OztcnM7Zk5mpmjq1ev7m+BkiQBK1d2137VqsHou236fdVPAGcAl2TmP/azb0mSurFuXb3t29p32/R7ROU44OnAoyLiwvLjsX2uQZKkBW3c2F37sbHB6Ltt+n3VzxcyMzLzNzPzQeXHv/WzBkmSqhgZKSZUq2JsrLeXBzfZd9s4hb4kSXMYH194tGJsDDZvHqy+28SgIknSHJYtK+Y0mZzce7+d5cv33m9ncrJYX8cU9k323Sbe60eSJDWqNTPTSpIkdcOgIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSWsugIkmSZjU1BevXw5o1sGJF8bh+fbG8XwwqkiRpH3v2wNgYrF0LZ5wBV10FN91UPJ5xRrF8bKxoV7dl9XchSZKWkk2bYNu2+dts2wYRsGVLvbX0dUQlIt4ZEVdHxMX97FeSJFUzNbVwSJm2dWv9h4H6fejnTOCEPvcpSZIq6naEZOvWeuqY1tegkpnnAT/pZ5+SJKm6HTvqbd+tVp5MGxGnRcREREzs3Lmz6XIkSRoau3d3137XrlrKuFUrg0pmbs/M0cwcXb16ddPlSJI0NFau7K79qlW1lHGrVgYVSZLUjHXr6m3fLYOKJEm61caN3bUfG6unjmn9vjz5LOB84H4RcUVEPKuf/UuSpPmNjMCGDdXajo0V7evU1wnfMvMp/exPkiR1b3y8mMxtvkuPx8Zg8+b6a/HQjyRJ2seyZcV8KpOTe+/1s3z53nv9TE4W65f1YbjDKfQlSdKsRkbg9NObrcERFUmS1FoGFUmS1FoGFUmS1FoGFUmS1FoGFUmS1FoGFUmS1FoGFUmS1FqRmU3XMK+I2Al8r+k6euwQ4Jqmi2jAMG73MG4zDOd2D+M2w3Bu9zBuM9S73ffKzNWzrWh9UBlEETGRmaNN19Fvw7jdw7jNMJzbPYzbDMO53cO4zdDcdnvoR5IktZZBRZIktZZBpRnbmy6gIcO43cO4zTCc2z2M2wzDud3DuM3Q0HZ7jookSWotR1QkSVJrGVT6KCLuGRGfjYhLIuIbEfG8pmvql4g4ICK+GhE7mq6lXyJiVUScHRGXlu/5w5uuqW4R8YLye/viiDgrIpY3XVMdIuKdEXF1RFw8Y9ldI+IzEfHt8vEuTdZYhzm2+x/K7/GLIuIjEbGqwRJ7brZtnrHuLyMiI+KQJmqr01zbHRGbIuK/y5/zN/ajFoNKf+0BXpiZDwAeBjwnIn6t4Zr65XnAJU0X0WdvAz6VmfcHHsiAb39EHA48FxjNzGOAA4AnN1tVbc4ETuhY9hLg3Mz8VeDc8vmgOZPbbvdngGMy8zeBbwEv7XdRNTuT224zEXFP4DHA5f0uqE/OpGO7I+L3gJOB38zMXwfe1I9CDCp9lJlXZuZU+fl1FH+4Dm+2qvpFxBHA44B3NF1Lv0TEnYFHAGcAZObPM3NXo0X1xzJgRUQsAw4CfthwPbXIzPOAn3QsPhl4d/n5u4En9LOmfphtuzPznMzcUz79EnBE3wur0RzvNcBbgBcBA3mi5xzbPQa8PjNvLttc3Y9aDCoNiYijgAcDFzRcSj+8leIH+pcN19FP9wZ2Au8qD3m9IyLu2HRRdcrMH1D8h3U5cCWwOzPPabaqvrp7Zl4JxT8lwKEN19OEPwM+2XQRdYuIk4AfZObXmq6lz+4L/E5EXBARn4+I3+pHpwaVBkTEwcCHgOdn5rVN11OniFgHXJ2Zk03X0mfLgBFga2Y+GPgZg3ko4FblORknA0cD9wDuGBFPa7Yq9UtEvJzi8PZ7mq6lThFxEPBy4G+arqUBy4C7UJy68FfAByIi6u7UoNJnEXF7ipDynsz8cNP19MFxwEkR8V3gfcCjIuJfmi2pL64ArsjM6RGzsymCyyB7NPC/mbkzM28BPgwc23BN/XRVRBwGUD72ZVi8DSLiFGAd8NQc/Dkv7kMRxr9W/l47ApiKiDWNVtUfVwAfzsKXKUbJaz+R2KDSR2XyPAO4JDP/sel6+iEzX5qZR2TmURQnVv5HZg78f9mZ+SPg+xFxv3LR8cA3GyypHy4HHhYRB5Xf68cz4CcQd/g4cEr5+SnAxxqspW8i4gTgxcBJmXlD0/XULTO/npmHZuZR5e+1K4CR8md+0H0UeBRARNwXuAN9uDmjQaW/jgOeTjGqcGH58dimi1JtNgHviYiLgAcBf99sOfUqR4/OBqaAr1P8fhnIGTwj4izgfOB+EXFFRDwLeD3wmIj4NsXVIK9vssY6zLHdbwfuBHym/J22rdEie2yObR54c2z3O4F7l5csvw84pR8jaM5MK0mSWssRFUmS1FoGFUmS1FoGFUmS1FoGFUmS1FoGFUmS1FoGFUmS1FoGFWkRIuJZ5e3dj+hY/oZy+dM6lj+mXL5fM7VGxFHl66xboN1fRESluQci4vER8dmIuDYifhYRX46IZ3ZOjR0RZ0bExIznp5a1HDzPa/9u2Wb646cR8YWIOL5KbYsREQeXfZ3a49c9NCJeVd6na+by6W08ppf9dfTxRxHxnYg4ICI+17FPZ/t4VUQcHhHXR8S966pL6geDirQ4XywfO4PHscANcyy/GWjVPY8i4sUUM6peQTFz8MkU23Y6sKWj+d8Bpy6yq6cCDweeBtwEfCoiHrTI12rKocArgaM6lk9RbNtldXQaEbcDXg38Q2b+AthY9jf9cSnwbx3L3lHeJPL9DOc9aTRAljVdgLREXUpxC/RjgQ/ArfdxWgu8m9mDysT07dEXIyKWL/Zr53i9tRSz5b4hM2feMPHfI+K/gS0R8enM/ChAZu7PH+KLMvPist/PA98Hng08Z5a6DgAOyMyf70d/fVPeWPRLNXZxPMX9Zd5b9rfPrRgi4mfAzsycrYZ3AedGxAsz88c11ijVxhEVaRHKaaPPZ99A8mAgKEYifiMi7gS3/kf8UPaOwhARfxoRX4+ImyPi+xHx2ohYNmP99GGVh5RD/TdS3K30NiLiwIh4e0TsioifRMRbgNtX2Iy/AK5j9qn9t1OMEDx3Rj/7HPpZrMy8HvgW5cjE9OtGxBMi4hsUIy4PLdf9RUR8u9xP34mIF3S+XnlY5FsRcWNEnAfcf5Y2GRF/0bHsVRFxTceye0XEWRFxTUTcEBEXRcT/KQ/3fL1s9tnpQyzl19zm0E8U9zvaHBE/ioibIuIrEfH7HX19LiLOLl//O+Wht09Gx+FEivsGnZOZ1y24c2/rvygC9ZMX8bVSKxhUpMX7IvCgiFhRPn84xaGdi4FdlH9sgV8HVlL80aD8g/V+ikMGJwPjwF9S3DOl01nADuCx5eNsXg+spzg081TgXsALK9T/CIqbRF7buaI8xPCvwLEzA1QvlCMm9wRm3sTtKOCNwOsotvV/I+LZFPvm48DjgQ8Cb46Il8x4rRGKffk14A/Lth9YZF2HUoTP36J4Px5PcRPRewJXUuxbKEaBpg+xzOV04JnAa4EnUowgfSIifruj3UMpAuMLgdMo7rDdeX+kRzEj5HajDNRforiztbQkeehHWrwvUoxc/BZwHsXoyvmZmRHxpfL5v7N31GX6j83fAp/LzOk77X6qPG/1dRHxmsy8YkYfmzPzbdNPZjmR827ABuCVmfnmctmnqXan5sMp/rDP5XvAgcDdgKsqvN58DigDz12BlwOHAR+Zsf5uwKMz80K4dRTqVcCZmTkdus6JiJXASyPirZl5E/ASitGZPy3/KH8yIg4EXrOIGl9AESjXZuaV5bJzp1dGcXNJgG/OcZhlut0DgKcAz8zMd5fLPg1cBLwC+IMZze8MPC4zf1q2WwO8JSJWZOaNEXEPin118SK2Z9rXKA6zSUuSIyrS4n0Z2MPeIHIsxX/kUPwXO3P5tzNzZzmaMEIxOjDT+yl+Hjv/S//EAjX8BrAc+Nj0gsz85cznLXEhcAtF4HkW8OLMnDlC9IPpkFI6ArgHs++nO1NsN8BDgI933MH1w4us8VHAp2aElMX6LYpDgLfWXr4nHwQ6R1S+Mh1SStMB8/DycU35uM8hqi5dAxwase9VXNJS4YiKtEiZeUNEXEhxeOQIij+u00HlfOCF5cjAscAXyuWHUIzCdI5QTD+/6xzL5zL9h+zqjuWdz2fzA4rDRHO5F8WVSr04CfPJFOe8/BT4Xmbu6VjfuZ2HzbG8cz+tYXHbPpu7AV9Z5NfOdBhwfWbe0LH8KuCgiDhwxknVuzraTJ9AvLzjcdEnYZdfu6z8uGU/XkdqhCMq0v75IsUoyLHAd2f8N34BcCfgkcCvUJ6fQvHf7S0Ul7rOdPfy8ScdyxeaC2X6PI/O1+t8PpvzgN+dPul3pjJgPQ744iyhYjG+kZkTmXnZHK/XuZ3T+3Gh/fSjWdrMtu03A3foWNYZCn/M3oC0P64EDo6IgzqW3x24ocsrv6a3c9V+1LOKIjgZUrQkGVSk/fNfFKMkp7B3NIXyCo1vUJyUCeX5KeVJqpPAn3S8zp8Cv5z5GhV9neIqmZOnF5Qh4+Q5v2Kvt1Ock/HSWdatB34VeNss6/rhCuCHzL6frmXvFThfAU7qOKzxh3O83gOmn5T76FEdbc4F/iAi7s7sOkc75vIViuD1xzP6i/L5F+b6ojn8b9nv0V1+3UxHUZzHIy1JHvqR9s/0SMmJwPM61p1PcRLjT4FLZix/JfDpiHgX8D6K8y3+Dji940TaBWXmjyNiO/DqiNhDEY6eDcw5W+yMr52MiJcBr4+Iw8tafg6so7gSZVtmNnKuS2b+MiJeBfy/iPgx8BmK0akx4GXlibQAb6AYvfpARJwBHENxDkynjwDPiYivAv9DEcTu3NHmLcAzgP+MiNdSXKnzAOCOmflG4HLgRuCUiNgN3JKZt7lcOzMviYizgLdHxJ2B71C8J/cv6+9mP9wcEZMU8/O8q5uvnWGUvd+n0pLjiIq0H8rZPy+nOHmyczTk/OnlM0/2zMxzKM7ZGKW4BPj5wJspwsFivAh4J8UMpGdRjET8Y8X63wCcRHE+ygfKeo6juFR24yLr6YnMPJ1iHpcnUlya/RTghZn5+hltJij25YOBjwJPAJ40y8u9muJk1tcAZ1Kc3PvOjv52Umz7V4G3ln2eRvH+UoajZ1OEhs8z//ksz6aY+O8VFCc23wtYl5ndjqhAcXLwCYv4OiLiEIp6P7SYr5faIPY9WV6S1CbloajLgd/OzK5O9o2IP6c4/Hjf9Je9lihHVCSpxTLzKuAd3PbQ4rzK82KeB7zWkKKlzKAiSe33d8Al5Tw8Va0B3gP8cz0lSf3hoR9JktRajqhIkqTWMqhIkqTWMqhIkqTWMqhIkqTWMqhIkqTW+v9ETYOCYT0UBQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.array([[1,8],[2, 7], [3,6],[4,8],[5,8],[6,7],[7,7],[8,5],[9,5],[10,6],[11,4],[12,5],[13,3],[14,2],[15,2],[16,1]])\n",
    "plt.subplot(1,2,1)\n",
    "plt.scatter(X[:,0],X[:,1],color='b',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('World Oil Production(T)',fontsize=15)\n",
    "plt.ylabel('Gasoline prices(T)',fontsize=15)\n",
    "plt.gcf().set_size_inches((20,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.5 Pearson's Correlation\n",
    "\n",
    "Shell we take into account the variance? An alternative is to divide the deviations by $\\sigma$, which yields standard scores, and compute the product of standard scores:\n",
    "\n",
    "$$ p_i = \\frac{(x_i - \\mu_X)}{\\sigma_X} \\frac{(y_i - \\mu_Y)}{\\sigma_Y} $$\n",
    " \n",
    "The mean of these products is:\n",
    "\n",
    "$$ \\rho = \\frac{1}{n} \\sum p_i = \\frac{1}{n} \\sum  \\frac{(x_i - \\mu_X)}{\\sigma_X} \\frac{(y_i - \\mu_Y)}{\\sigma_Y}  $$\n",
    "\n",
    "Or we can rewrite $\\rho$ by factoring out $\\sigma_X$ and $\\sigma_Y$:\n",
    "\n",
    "$$ \\rho = \\frac{Cov(X,Y)}{\\sigma_X \\sigma_Y}$$\n",
    "\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corr(X, X) = 2.00000\n",
      "Corr(X, Y) = 0.00009\n"
     ]
    }
   ],
   "source": [
    "def Corr(X, Y):\n",
    "    assert len(X) == len(Y)\n",
    "    return Cov(X, Y) / np.prod([np.std(V) for V in [X, Y]])\n",
    "\n",
    "print(\"Corr(X, X) = %.5f\" % Corr(X, X))\n",
    "\n",
    "Y=np.random.random(len(X))\n",
    "\n",
    "print(\"Corr(X, Y) = %.5f\" % Corr(X, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When $\\rho = 0$, we cannot say that there is no relationship between the variables!\n",
    "\n",
    "Pearson's coefficient only measures **linear** correlations!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.6 Spearman’s rank correlation\n",
    "\n",
    "Pearson’s correlation works well if the relationship between variables is linear and if the variables are roughly normal. But it is not robust in the presence of **outliers**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spearman’s rank correlation is an alternative that mitigates the effect of outliers and skewed distributions. To compute Spearman’s correlation, we have to compute the rank of each value, which is its index in the sorted sample. \n",
    "\n",
    "For example, in the sample {7, 1, 2, 5} the rank of the value 5 is 3, because it appears third if we sort the elements. \n",
    "\n",
    "Then, we compute the Pearson’s correlation, **but for the ranks**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ranks:  [4.0, 1.0, 2.0, 3.0]\n",
      "Pearson rank coefficient: 0.28\n",
      "[1.0, 2.0, 3.0, 4.0, 5.0]\n",
      "[2.0, 1.0, 3.0, 5.0, 4.0]\n",
      "Spearman rank coefficient: 0.80\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def list2rank(l):\n",
    "    #l is a list of numbers\n",
    "    # returns a list of 1-based index; mean when multiple instances\n",
    "    return [np.mean([i+1 for i, sorted_el in enumerate(sorted(l)) if sorted_el == el]) for el in l]\n",
    "\n",
    "l = [7, 1, 2, 5]\n",
    "print(\"ranks: \", list2rank(l))\n",
    "\n",
    "def spearmanRank(X, Y):\n",
    "    # X and Y are same-length lists\n",
    "    print(list2rank(X))\n",
    "    print(list2rank(Y))\n",
    "    return Corr(list2rank(X), list2rank(Y))\n",
    "\n",
    "X = [10, 20, 30, 40, 1000]\n",
    "Y = [-70, -1000, -50, -10, -20]\n",
    "plt.plot(X,'ro')\n",
    "plt.plot(Y,'go')\n",
    "\n",
    "print(\"Pearson rank coefficient: %.2f\" % Corr(X, Y))\n",
    "print(\"Spearman rank coefficient: %.2f\" % spearmanRank(X, Y))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Obtain for the Anscombe's quartet [2] given in the figures bellow, the different estimators (mean, variance, covariance for each pair, Pearson's correlation and Spearman's rank correlation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.array([[10.0, 8.04, 10.0, 9.14, 10.0, 7.46, 8.0, 6.58],\n",
    "[8.0, 6.95, 8.0, 8.14, 8.0, 6.77, 8.0, 5.76],\n",
    "[13.0,7.58,13.0,8.74,13.0,12.74,8.0,7.71],\n",
    "[9.0,8.81,9.0,8.77,9.0,7.11,8.0,8.84],\n",
    "[11.0,8.33,11.0,9.26,11.0,7.81,8.0,8.47],\n",
    "[14.0,9.96,14.0,8.10,14.0,8.84,8.0,7.04],\n",
    "[6.0,7.24,6.0,6.13,6.0,6.08,8.0,5.25],\n",
    "[4.0,4.26,4.0,3.10,4.0,5.39,19.0,12.50],\n",
    "[12.0,10.84,12.0,9.13,12.0,8.15,8.0,5.56],\n",
    "[7.0,4.82,7.0,7.26,7.0,6.42,8.0,7.91],\n",
    "[5.0,5.68,5.0,4.74,5.0,5.73,8.0,6.89]])\n",
    "\n",
    "\n",
    "plt.subplot(2,2,1)\n",
    "plt.scatter(X[:,0],X[:,1],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "\n",
    "plt.subplot(2,2,2)\n",
    "plt.scatter(X[:,2],X[:,3],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "\n",
    "plt.subplot(2,2,3)\n",
    "plt.scatter(X[:,4],X[:,5],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "\n",
    "plt.subplot(2,2,4)\n",
    "plt.scatter(X[:,6],X[:,7],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "plt.gcf().set_size_inches((10,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Main reference\n",
    "[1] *Think Stats: Probability and Statistics for Programmers*, by Allen B. Downey, published by O'Reilly Media.\n",
    "http://www.greenteapress.com/thinkstats/\n",
    "\n",
    "[2] Anscombe's quartet, https://en.wikipedia.org/wiki/Anscombe%27s_quartet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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