lab7_hw.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Домашня робота №7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Перетворення випадкових величин"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.stats import uniform, expon, norm, geom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 Квантильне перетворення"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Задана щільність"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нехай випадкова величина $\\xi$ має щільність\n",
    "$f(x) = a \\sin(x) I_{[0, \\pi]}(x),$\n",
    "де $I_{[c, d]}(x)$ - індикатор на відрізку $[c, d]$.\n",
    "\n",
    "Знайдіть значення параметра $a$.\n",
    "\n",
    "Згенеруйте $n = 100000$ значень випадкової величини $\\xi$ за допомогою квантильного перетворення.\n",
    "\n",
    "Намалюйте нормовану гістограму отриманих $n = 100000$ значень випадкової величини $\\xi$ разом з її функцією щільності."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# функція щільності xi\n",
    "def density_f(x):\n",
    "    a = 0.5\n",
    "    return a * np.sin(x)\n",
    "\n",
    "# функція, обернена до функції розподілу xi\n",
    "def rfunc(y):\n",
    "    return np.arccos(1 - 2 * y)\n",
    "\n",
    "fig, axs = plt.subplots(1,1, figsize=(20,5))\n",
    "\n",
    "eta = uniform(loc=0, scale=1)\n",
    "\n",
    "lst_f = rfunc(eta.rvs(size=10 ** 5))\n",
    "axs.hist(lst_f, normed=True, bins=100)\n",
    "x = np.arange(0, np.pi, 0.01)\n",
    "axs.plot(x, density_f(x), color='r', lw=3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Нормальний розподіл"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нехай випадкова величина $\\xi \\sim N(0, 1)$.\n",
    "\n",
    "Згенеруйте $n = 100000$ значень випадкової величини $\\xi$ за допомогою квантильного перетворення.\n",
    "\n",
    "Намалюйте нормовану гістограму отриманих $n = 100000$ значень випадкової величини $\\xi$ разом з її функцією щільності."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1,1, figsize=(20,5))\n",
    "\n",
    "xi = norm(0, 1)\n",
    "eta = uniform(loc=0, scale=1)\n",
    "\n",
    "vals_eta = eta.rvs(size=100000)\n",
    "vals_xi = xi.ppf(vals_eta)\n",
    "axs.hist(vals_xi, normed=True, bins=100)\n",
    "x = np.arange(-4, 4, 0.1)\n",
    "axs.plot(x, xi.pdf(x), 'r', lw=4)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Відсутність пам'яті"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Розглянемо випадкову величину $\\xi$ з геометричного розподілу з параметром $p = 0.5$.\n",
    "Тобто $\\xi \\sim Geom(0.5)$.\n",
    "\n",
    "1. Згенеруйте $n = 10000$ значень випадкової величини $\\xi$;\n",
    "2. Реалізуйте 2 сабплоти в одному рядку;\n",
    "3. На першому сабплоті намалюйте:\n",
    "   - нормовану гістограму згенерованих $n = 10000$ значень випадкової величини $\\xi$;\n",
    "   - функцію ймовірностей випадкової величини $\\xi$;\n",
    "4. Отримайте $n = 10000$ значень випадкової величини $\\eta = (\\xi - 1) I_{(\\xi - 1) > 0}$;\n",
    "5. На другому сабплоті намалюйте:\n",
    "   - нормовану гістограму отриманих значень випадкової величини $\\eta$;\n",
    "   - функцію ймовірностей випадкової величини $\\xi$.\n",
    "\n",
    "**Зауваження 1.** Графік функції ймовірнстей краще малювати для $10$ значень.\n",
    "\n",
    "**Зауваження 2.** У гістограмах проміжок значень слід розбивати на одиничні інтервали."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1,2, figsize=(20,5))\n",
    "\n",
    "xi = geom(0.5)\n",
    "vals = xi.rvs(size=10000)\n",
    "x = np.arange(1, 11)\n",
    "axs[0].hist(vals, normed=True, bins=x)\n",
    "axs[0].plot(x, xi.pmf(x), 'r', lw=3)\n",
    "\n",
    "axs[1].hist(xi.rvs(size=10000) - 1, normed=True, bins=x)\n",
    "axs[1].plot(x, xi.pmf(x), 'r', lw=3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 Задача 1.11.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Розглянемо випадкову величину $\\xi$ зі стандартного експоненційного розподілу.\n",
    "Тобто $\\xi \\sim Exp(1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Експонента"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Згенеруйте $n = 10000$ значень випадкової величини $\\xi$;\n",
    "2. Реалізуйте 2 сабплоти в одному рядку;\n",
    "3. На першому сабплоті намалюйте:\n",
    "   - нормовану гістограму згенерованих $n = 10000$ значень випадкової величини $\\xi$;\n",
    "   - функцію щільності випадкової величини $\\xi$;\n",
    "4. Отримайте $n = 10000$ значень випадкової величини $\\eta = \\exp\\{-\\xi\\}$ (застосуйте функцію модуль до згенерованих $n = 10000$ значень випадкової величини $\\xi$);\n",
    "5. На другому сабплоті намалюйте:\n",
    "   - нормовану гістограму отриманих $n = 10000$ значень випадкової величини $\\eta$;\n",
    "   - функцію щільності випадкової величини $\\xi$;\n",
    "   - функцію щільності випадкової величини $\\eta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func1(xi):\n",
    "    return np.exp(-xi)\n",
    "\n",
    "\n",
    "def denc1(y):\n",
    "    return np.ones((1, len(y)))\n",
    "\n",
    "fig, axs = plt.subplots(1,2, figsize=(20,5))\n",
    "\n",
    "xi = expon(loc=0, scale=1)\n",
    "xi_rvs = xi.rvs(size=10000)\n",
    "\n",
    "x1 = np.arange(0, 6, 0.1)\n",
    "axs[0].hist(xi_rvs, normed=True, bins=100)\n",
    "axs[0].plot(x1, xi.pdf(x1), 'r', lw=3)\n",
    "axs[0].set_xlim(-0.1, 6.1)\n",
    "\n",
    "axs[1].hist(func1(xi_rvs), normed=True, bins=50, color='c')\n",
    "axs[1].plot(x1, xi.pdf(x1), 'r', lw=3)\n",
    "x2 = np.arange(0, 1.1, 0.1)\n",
    "axs[1].plot(x2, denc1(x2)[0], 'b', lw=4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Квадрат"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Згенеруйте $n = 10000$ значень випадкової величини $\\xi$;\n",
    "2. Реалізуйте 2 сабплоти в одному рядку;\n",
    "3. На першому сабплоті намалюйте:\n",
    "   - нормовану гістограму згенерованих $n = 10000$ значень випадкової величини $\\xi$;\n",
    "   - функцію щільності випадкової величини $\\xi$;\n",
    "4. Отримайте $n = 10000$ значень випадкової величини $\\eta = \\xi^2$ (застосуйте функцію модуль до згенерованих $n = 10000$ значень випадкової величини $\\xi$);\n",
    "5. На другому сабплоті намалюйте:\n",
    "   - нормовану гістограму отриманих $n = 10000$ значень випадкової величини $\\eta$;\n",
    "   - функцію щільності випадкової величини $\\xi$;\n",
    "   - функцію щільності випадкової величини $\\eta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func2(xi):\n",
    "    return xi ** 2\n",
    "\n",
    "\n",
    "def denc2(y):\n",
    "    return np.exp(-y ** 0.5) / (2 * y ** 0.5)\n",
    "\n",
    "fig, axs = plt.subplots(1,2, figsize=(20,5))\n",
    "\n",
    "xi_rvs = xi.rvs(size=10000)\n",
    "x1 = np.arange(0, 6, 0.1)\n",
    "axs[0].hist(xi_rvs, normed=True, bins=100)\n",
    "axs[0].plot(x1, xi.pdf(x1), 'r', lw=3)\n",
    "axs[0].set_xlim(-0.1, 6.1)\n",
    "\n",
    "axs[1].hist(func2(xi_rvs), normed=True, bins=np.arange(0, 3, 0.2), color='c')\n",
    "x2 = np.arange(0.01, 3.01, 0.01)\n",
    "axs[1].plot(x1, xi.pdf(x1), 'r', lw=3)\n",
    "axs[1].plot(x2, denc2(x2), 'b', lw=4)\n",
    "axs[1].set_ylim(0, 2.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 Задача 1.11.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Розглянемо випадкову величину $\\xi$ зі стандартного рівномірного розподілу.\n",
    "Тобто $\\xi \\sim Unif(0, 1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Лінійне перетворення"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Згенеруйте $n = 10000$ значень випадкової величини $\\xi$;\n",
    "2. Реалізуйте 2 сабплоти в одному рядку;\n",
    "3. На першому сабплоті намалюйте:\n",
    "   - нормовану гістограму згенерованих $n = 10000$ значень випадкової величини $\\xi$;\n",
    "   - функцію щільності випадкової величини $\\xi$;\n",
    "4. Отримайте $n = 10000$ значень випадкової величини $\\eta = 3 \\xi - 2$ (застосуйте функцію модуль до згенерованих $n = 10000$ значень випадкової величини $\\xi$);\n",
    "5. На другому сабплоті намалюйте:\n",
    "   - нормовану гістограму отриманих $n = 10000$ значень випадкової величини $\\eta$;\n",
    "   - функцію щільності випадкової величини $\\xi$;\n",
    "   - функцію щільності випадкової величини $\\eta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABIQAAAEyCAYAAACLeQv5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAHaZJREFUeJzt3XGMpOddH/DvLz5MJAgJzS2Q+u5yrrhUcQMl0daAgpSjSaqzQb62AWS3aTE1uaJioEpKawQyyPknISqIqibhCJYhKjYmKvSKj5o02LKAOPWmARPbOFydFJ9J68MYS1UajMuvf+wYjde3t7Pe2dmZeT8f6XTzvu+jmd8+++7sO999nuet7g4AAAAAw/GSvS4AAAAAgNkSCAEAAAAMjEAIAAAAYGAEQgAAAAADIxACAAAAGBiBEAAAAMDAbBkIVdUtVfVEVX1qk+P/uKoeqKrfr6rfqaq/Pf0yAQAAAJiWSUYI3Zrk2AWOfybJm7r7a5K8O8nJKdQFAAAAwC7Zt1WD7r63qg5f4PjvjG3el+TAzssCAAAAYLdsGQht03VJfn2Shvv37+/Dhw9P+eUBgHnxiU984k+6e2Wv6+D5XIMBwHKb9BpsaoFQVX1z1gOhb7pAmxNJTiTJoUOHsra2Nq2XBwDmTFX9z72ugRc6fPiwazAAWGKTXoNN5S5jVfW1ST6Y5Hh3P7lZu+4+2d2r3b26suIPhgAAAAB7YceBUFUdSvIfk/yT7v70zksCAAAAYDdtOWWsqm5LcjTJ/qo6m+RHk3xRknT3B5LcmOSVSX66qpLk2e5e3a2CAQAAANiZSe4yds0Wx787yXdPrSIAAAAAdtVU1hACAAAAYHEIhAAAAAAGRiAEAAAAMDACIQAAAICBEQgBAAAADIxACAAAAGBgBEIAAAAAA7NvrwuAcYdvuHPLNp99z7fMoBIAAABYXgKhKRBiAAAAAItEILSABFAAAADATlhDCAAAAGBgBEIAAAAAAyMQAgAAABgYgRAAAADAwAiEAAAAAAZGIAQAMIeq6paqeqKqPrXJ8aqqf1dVZ6rqgap6w6xrBAAWl0AIAGA+3Zrk2AWOX5HkyOjfiSTvn0FNAMCSEAgBAMyh7r43yZ9eoMnxJL/Q6+5L8oqqetVsqgMAFt2+vS4AAIAX5ZIkj41tnx3t+9zelAOwBKr2ugKGpnvPXlogBLCkDt9w51Se57Pv+ZapPA/TNcn31/eO51TViaxPK8uhQ4f2uBoAYB6YMgYAsJgeT3JwbPvAaN8LdPfJ7l7t7tWVlZWZFAcAzDcjhAAAFtOpJNdX1e1Jvj7J091tuhjATuzh9B2YNYEQAMAcqqrbkhxNsr+qzib50SRflCTd/YEkp5NcmeRMks8n+a69qRQAWEQCIQCAOdTd12xxvJN874zKAQCWzFIGQhbaBAAAANjcUgZCALMmiAYAABaJu4wBAAAADIwRQgAsrXkbuTVJPcn0apq3rx8AgPkhEOKCfJgAAACA5WPKGAAAAMDAGCEEwAVNOs1pEkYUAgDAfBAIAXPFNEV9sKimGZwBAMBuM2UMAAAAYGCMEIIFZATJYjKCZHr0JQAA7IxACAC2IIACAGDZCIRgRozqAQAAYF5sGQhV1S1JvjXJE939uvMcryQ/leTKJJ9Pcm13//dpFwoAu8HoHwAAhmiSRaVvTXLsAsevSHJk9O9EkvfvvCwAAAAAdsuWgVB335vkTy/Q5HiSX+h19yV5RVW9aloFAgAAADBd1d1bN6o6nOTXNpky9mtJ3tPdvzXa/miSf9Pdaxd6ztXV1V5bu2CTF6dq+s8JAMtuguuB7aqqT3T36tSfmB3ZtWswAGAuTHoNNsmUsampqhNVtVZVa+fOnZvlSwMAAAAwMo1A6PEkB8e2D4z2vUB3n+zu1e5eXVlZmcJLAwAAALBd07jt/Kkk11fV7Um+PsnT3f25KTzvi9M989t7L/PrLfPXNmvT/Nr002y/tnm8C9UkfbCodU9iHr+2aZrl93dR3ysAANiZSW47f1uSo0n2V9XZJD+a5IuSpLs/kOR01m85fybrt53/rt0qdpHN44dcJuN7BwAAwLLZMhDq7mu2ON5JvndqFc2ZRf0rtBADAAAA2Mw0powBwESE1QAAMB9mepcxAAAAAPaeEUJzZFGnpwEAAACLRSDEzAi8YHr8PAEAADshEBowHyhZ1PVcFrVuAACAeSEQAgZNMMo8cl4CALDbBEIwR3wIBAAAYBbcZQwAAABgYIwQYuFYPwYAAAB2RiAEXNCk09gmCeFMiWMSzhMAANh9powBAAAADIwRQuyYv+bPp6F/X4b+9QMAAFyIEUIAAAAAA2OEEEyB0SgAAAAsEoEQgybIAQAAYIgEQiwlQQ8AAABszhpCAAAAAAMjEAIAAAAYmMFOGTOlCAAAABgqI4QAAAAABkYgBAAwp6rqWFU9UlVnquqG8xw/VFV3V9Unq+qBqrpyL+oEABbPYKeMAdNlGibAdFXVRUluTvLWJGeT3F9Vp7r7obFmP5Lkju5+f1VdluR0ksMzLxYAWDhGCAEAzKfLk5zp7ke7+5kktyc5vqFNJ/my0eOXJ/njGdYHACwwgRAAwHy6JMljY9tnR/vG/ViSt1fV2ayPDvq+8z1RVZ2oqrWqWjt37txu1AoALBiBEADA4romya3dfSDJlUk+VFUvuL7r7pPdvdrdqysrKzMvEgCYPwIhAID59HiSg2PbB0b7xl2X5I4k6e6PJXlpkv0zqQ4AWGgCIQCA+XR/kiNVdWlVXZzk6iSnNrT5oyRvTpKqem3WAyFzwgCALQmEAADmUHc/m+T6JHcleTjrdxN7sKpuqqqrRs3eleQdVfV7SW5Lcm13995UDAAsEredBwCYU919OuuLRY/vu3Hs8UNJ3jjrugCAxWeEEAAAAMDACIQAAAAABkYgBAAAADAwAiEAAACAgREIAQAAAAyMQAgAAABgYARCAAAAAAMjEAIAAAAYmIkCoao6VlWPVNWZqrrhPMcPVdXdVfXJqnqgqq6cfqkAAAAATMOWgVBVXZTk5iRXJLksyTVVddmGZj+S5I7ufn2Sq5P89LQLBQAAAGA6JhkhdHmSM939aHc/k+T2JMc3tOkkXzZ6/PIkfzy9EgEAAACYpkkCoUuSPDa2fXa0b9yPJXl7VZ1NcjrJ953viarqRFWtVdXauXPnXkS5AAAAAOzUtBaVvibJrd19IMmVST5UVS947u4+2d2r3b26srIypZcGAAAAYDsmCYQeT3JwbPvAaN+465LckSTd/bEkL02yfxoFAgAAADBdkwRC9yc5UlWXVtXFWV80+tSGNn+U5M1JUlWvzXogZE4YAAAAwBzaMhDq7meTXJ/kriQPZ/1uYg9W1U1VddWo2buSvKOqfi/JbUmu7e7eraIBAAAAePH2TdKou09nfbHo8X03jj1+KMkbp1saAAAAALthWotKAwAAALAgBEIAAAAAAyMQAgAAABgYgRAAAADAwAiEAAAAAAZGIAQAAAAwMAIhAAAAgIERCAEAAAAMjEAIAAAAYGAEQgAAAAADIxACAAAAGBiBEAAAAMDACIQAAAAABkYgBAAAADAwAiEAAACAgREIAQAAAAyMQAgAAABgYARCAAAAAAMjEAIAAAAYGIEQAAAAwMAIhAAAAAAGRiAEAAAAMDACIQAAAICBEQgBAMypqjpWVY9U1ZmqumGTNt9RVQ9V1YNV9YuzrhEAWEz79roAAABeqKouSnJzkrcmOZvk/qo61d0PjbU5kuSHkryxu5+qqq/Ym2oBgEVjhBAAwHy6PMmZ7n60u59JcnuS4xvavCPJzd39VJJ09xMzrhEAWFACIQCA+XRJksfGts+O9o17TZLXVNVvV9V9VXVsZtUBAAvNlDEAgMW1L8mRJEeTHEhyb1V9TXf/2XijqjqR5ESSHDp0aNY1AgBzyAghAID59HiSg2PbB0b7xp1Ncqq7/6K7P5Pk01kPiJ6nu09292p3r66srOxawQDA4hAIAQDMp/uTHKmqS6vq4iRXJzm1oc2vZn10UKpqf9ankD06yyIBgMUkEAIAmEPd/WyS65PcleThJHd094NVdVNVXTVqdleSJ6vqoSR3J/nB7n5ybyoGABaJNYQAAOZUd59OcnrDvhvHHneSd47+AQBMzAghAAAAgIERCAEAAAAMjEAIAAAAYGAEQgAAAAADM1EgVFXHquqRqjpTVTds0uY7quqhqnqwqn5xumUCAAAAMC1b3mWsqi5KcnOStyY5m+T+qjrV3Q+NtTmS5IeSvLG7n6qqr9itggEAAADYmUlGCF2e5Ex3P9rdzyS5PcnxDW3ekeTm7n4qSbr7iemWCQAAAMC0TBIIXZLksbHts6N9416T5DVV9dtVdV9VHTvfE1XViapaq6q1c+fOvbiKAQAAANiRaS0qvS/JkSRHk1yT5Ger6hUbG3X3ye5e7e7VlZWVKb00AAAAANsxSSD0eJKDY9sHRvvGnU1yqrv/ors/k+TTWQ+IAAAAAJgzkwRC9yc5UlWXVtXFSa5OcmpDm1/N+uigVNX+rE8he3SKdQIAAAAwJVsGQt39bJLrk9yV5OEkd3T3g1V1U1VdNWp2V5Inq+qhJHcn+cHufnK3igYAAADgxdvytvNJ0t2nk5zesO/Gsced5J2jfwAAAADMsWktKg0AAADAghAIAQAAAAyMQAgAAABgYARCAAAAAAMjEAIAAAAYGIEQAAAAwMAIhAAAAAAGRiAEAAAAMDACIQAAAICBEQgBAAAADIxACAAAAGBgBEIAAAAAAyMQAgAAABgYgRAAAADAwAiEAAAAAAZGIAQAAAAwMAIhAAAAgIERCAEAAAAMjEAIAAAAYGAEQgAAAAADIxACAAAAGBiBEAAAAMDACIQAAAAABkYgBAAAADAwAiEAAACAgREIAQAAAAyMQAgAAABgYARCAAAAAAMjEAIAmFNVdayqHqmqM1V1wwXava2quqpWZ1kfALC4BEIAAHOoqi5KcnOSK5JcluSaqrrsPO1eluQHknx8thUCAItMIAQAMJ8uT3Kmux/t7meS3J7k+HnavTvJe5N8YZbFAQCLTSAEADCfLkny2Nj22dG+v1JVb0hysLvvvNATVdWJqlqrqrVz585Nv1IAYOEIhAAAFlBVvSTJTyR511Ztu/tkd6929+rKysruFwcAzD2BEADAfHo8ycGx7QOjfc95WZLXJbmnqj6b5BuSnLKwNAAwCYEQAMB8uj/Jkaq6tKouTnJ1klPPHezup7t7f3cf7u7DSe5LclV3r+1NuQDAItm31wUAAPBC3f1sVV2f5K4kFyW5pbsfrKqbkqx196kLPwNMru65Z8s2ffTortcBwOxMFAhV1bEkP5X1i5EPdvd7Nmn3tiQfTvJ3/HUKAGBnuvt0ktMb9t24Sdujs6hpnswyxJjktab5egCw27acMlZVFyW5OckVSS5Lck1VXXaedi9L8gNJPj7tIgEAAACYnknWELo8yZnufrS7n0lye5Lj52n37iTvTfKFKdYHAAAAwJRNEghdkuSxse2zo31/parekORgd995oSeqqhNVtVZVa+fOndt2sQAAAADs3I4Xla6qlyT5iSTXbtW2u08mOZkkq6urvdPXBgAAgHky6ZpjW7Em2XxapkX4Jxkh9HiSg2PbB0b7nvOyJK9Lck9VfTbJNyQ5VVWr0yoSAAAAgOmZZITQ/UmOVNWlWQ+Crk7yj5472N1PJ9n/3HZV3ZPkX7nLGADAsCzTX02BxeB9B168LQOh7n62qq5PclfWbzt/S3c/WFU3JVnr7lO7XSQAAAyJD7nAopp0ytws38Nm/Z66KO/hE60h1N2nk5zesO/GTdoe3XlZAAAAzMqifIDdLYsaYkzK947z2fGi0gAADFvVc4+Obt12qq88y9fb+rVm/XqL25fMp6NbtpjPc+Doli0mq3vr55n2c83SbL93RydqNev3561MXs90X6/38HZbkywqDQAAAMASEQgBAAAADIxACAAAAGBgrCEEAMCOPLf+wbQWpZ31AqGzrmlar7fsd8SZ5fk0zXNgURfvXdRzYNbm8T1sWpb5a5vEpOf3tPpgHt4rBEIAAAzaMn/AWeavDfaCnymWiUAIAABmyAdK5nE0ziQWdRQgTGKI56VACAAA2NKihhiTGOIHQQCBEAAALCAhxnya1vdlmgHcLM8V5+Xi8r0bHoEQAAAwM9P80OkDLMCLJxACAACmQkADsDgEQgAAzIzAAADmg0AIAABgAQlYgZ14yV4XAAAAAMBsCYQAAAAABkYgBAAAADAwAiEAAACAgREIAQAAAAyMQAgAAABgYARCAAAAAAMjEAIAAAAYGIEQAAAAwMAIhAAAAAAGRiAEAAAAMDACIQAAAICBEQgBAAAADIxACAAAAGBgBEIAAAAAAyMQAgAAABgYgRAAAADAwAiEAAAAAAZGIAQAAAAwMAIhAIA5VVXHquqRqjpTVTec5/g7q+qhqnqgqj5aVa/eizoBgMUjEAIAmENVdVGSm5NckeSyJNdU1WUbmn0yyWp3f22SDyf58dlWCQAsKoEQAMB8ujzJme5+tLufSXJ7kuPjDbr77u7+/GjzviQHZlwjALCgBEIAAPPpkiSPjW2fHe3bzHVJfv18B6rqRFWtVdXauXPnplgiALCoJgqEzF8HAJhfVfX2JKtJ3ne+4919srtXu3t1ZWVltsUBAHNpy0DI/HUAgD3xeJKDY9sHRvuep6rekuSHk1zV3X8+o9oAgAU3yQgh89cBAGbv/iRHqurSqro4ydVJTo03qKrXJ/mZrIdBT+xBjQDAgpokEJra/HUAACbT3c8muT7JXUkeTnJHdz9YVTdV1VWjZu9L8qVJfrmqfreqTm3ydAAAz7Nvmk82Nn/9TZscP5HkRJIcOnRomi8NALB0uvt0ktMb9t049vgtMy8KAFgKk4wQmtr8dQsaAgAAAOy9SQIh89cBAAAAlsiWgZD56wAAAADLZaI1hMxfBwAAAFgek0wZAwAAAGCJCIQAAAAABkYgBAAAADAwAiEAAACAgREIAQAAAAyMQAgAAABgYARCAAAAAAMjEAIAAAAYGIEQAAAAwMAIhAAAAAAGRiAEAAAAMDACIQAAAICBEQgBAAAADIxACAAAAGBgBEIAAAAAAyMQAgAAABgYgRAAAADAwAiEAAAAAAZGIAQAAAAwMAIhAAAAgIERCAEAAAAMjEAIAAAAYGAEQgAAAAADIxACAAAAGBiBEAAAAMDACIQAAAAABkYgBAAAADAwAiEAAACAgREIAQAAAAyMQAgAAABgYARCAAAAAAMjEAIAAAAYGIEQAAAAwMAIhAAAAAAGRiAEAAAAMDACIQAAAICBmSgQqqpjVfVIVZ2pqhvOc/yLq+qXRsc/XlWHp10oAMDQuAYDAHbLloFQVV2U5OYkVyS5LMk1VXXZhmbXJXmqu786yU8mee+0CwUAGBLXYADAbppkhNDlSc5096Pd/UyS25Mc39DmeJKfHz3+cJI3V1VNr0wAgMFxDQYA7JpJAqFLkjw2tn12tO+8bbr72SRPJ3nlNAoEABgo12AAwK7ZN8sXq6oTSU6MNv9PVT2ySy+1P8mf7NJz80L6e/b0+Wzp79nS3zNU793V/n71Lj0v2+QabK7ps+3TZ9unz7ZHf22fPtum2t0+m+gabJJA6PEkB8e2D4z2na/N2aral+TlSZ7c+ETdfTLJyUkK24mqWuvu1d1+Hdbp79nT57Olv2dLf8+W/p5rrsEGQJ9tnz7bPn22Pfpr+/TZ9s1Dn00yZez+JEeq6tKqujjJ1UlObWhzKsl3jh5/W5Lf7O6eXpkAAIPjGgwA2DVbjhDq7mer6vokdyW5KMkt3f1gVd2UZK27TyX5uSQfqqozSf406xcsAAC8SK7BAIDdNNEaQt19OsnpDftuHHv8hSTfPt3SdmTXh0TzPPp79vT5bOnv2dLfs6W/55hrsEHQZ9unz7ZPn22P/to+fbZ9e95nZVQxAAAAwLBMsoYQAAAAAEtEIAQAAAAwMAsdCFXVsap6pKrOVNUN5zn+xVX1S6PjH6+qw7OvcnlM0N/vrKqHquqBqvpoVb16L+pcFlv191i7t1VVV5XbPO7QJH1eVd8xOs8frKpfnHWNy2SC95RDVXV3VX1y9L5y5V7UuSyq6paqeqKqPrXJ8aqqfzf6fjxQVW+YdY0snqp6X1X9weic+ZWqesUm7Sb6nTYEVfXto98hf3mh391V9dmq+v2q+t2qWptljfNmG33mPBupqr9WVR+pqj8c/f/lm7T7f6Nz7HerauNdDJeez5PbN0GfXVtV58bOq+/eizrnxbxffy1sIFRVFyW5OckVSS5Lck1VXbah2XVJnurur07yk0neO9sql8eE/f3JJKvd/bVJPpzkx2db5fKYsL9TVS9L8gNJPj7bCpfPJH1eVUeS/FCSN3b330ryL2de6JKY8Bz/kSR3dPfrs37npJ+ebZVL59Ykxy5w/IokR0b/TiR5/wxqYvF9JMnrRr/7P53198jnmfR32oB8Ksk/THLvBG2/ubu/rruH/kefLfvMefYCNyT5aHcfSfLR0fb5/N/ROfZ13X3V7Mrbez5Pbt82fs5+aey8+uBMi5w/t2aOr78WNhBKcnmSM939aHc/k+T2JMc3tDme5OdHjz+c5M1VVTOscZls2d/dfXd3f360eV+SAzOucZlMcn4nybuz/ovpC7MsbklN0ufvSHJzdz+VJN39xIxrXCaT9Hcn+bLR45cn+eMZ1rd0uvverN+WfDPHk/xCr7svySuq6lWzqY5F1d2/0d3PjjY3+90/6e+0Qejuh7v7kb2uY5FM2GfOs+cb/xz080n+/h7WMq98ntw+P2fbNO/XX4scCF2S5LGx7bOjfedtM7pYeTrJK2dS3fKZpL/HXZfk13e1ouW2ZX+PhhMe7O47Z1nYEpvkHH9NktdU1W9X1X1VdaG0nwubpL9/LMnbq+ps1m+7/X2zKW2wtvs+Dxv9s5z/d79z68XpJL9RVZ+oqhN7XcwCcJ4931d29+dGj/9Xkq/cpN1Lq2ptdF0ztNDI58ntm/Tn7G2j6U8frqqDsyltYe3pe9e+Wb0Qw1FVb0+ymuRNe13LsqqqlyT5iSTX7nEpQ7Mv68M5j2b9r+D3VtXXdPef7WlVy+uaJLd297+tqm9M8qGqel13/+VeFwZDUlX/NclXnefQD3f3fxq1+eEkzyb5D7OsbV5N0mcT+KbufryqviLJR6rqD0Z/aV5KU+qzQblQn41vdHdXVW/yNK8enWd/I8lvVtXvd/f/mHatDMp/TnJbd/95Vf3zrI+w+rt7XBObWORA6PEk42njgdG+87U5W1X7sj7l4MnZlLd0JunvVNVbsv5L6E3d/eczqm0ZbdXfL0vyuiT3jEatflWSU1V1VXcPeuHJHZjkHD+b5OPd/RdJPlNVn856QHT/bEpcKpP093UZzbnu7o9V1UuT7E9iqt7umOh9nuHp7rdc6HhVXZvkW5O8ubvP96FzcOfWVn024XM8Pvr/iar6laxP1VjaQGgKfeY8G1NV/7uqXtXdnxtNPznv786x8+zRqronyeuTDCUQ8nly+7bss+4e758PxrqyW9nT965FnjJ2f5IjVXVpVV2c9QVHN66MfyrJd44ef1uS39zkQoWtbdnfVfX6JD+T5Cprq+zYBfu7u5/u7v3dfbi7D2d93QZh0M5M8p7yq1kfHZSq2p/1KWSPzrLIJTJJf/9RkjcnSVW9NslLk5ybaZXDcirJPx3d7eIbkjw9Nt0Azms0dfZfZ/130Oc3aTbJzztjqupLRjeOSFV9SZK/l/WFldmc8+z5xj8HfWeSF4yyqqovr6ovHj3en+SNSR6aWYV7z+fJ7ZvkM+H4+jdXJXl4hvUtoj29/lrYQGg0h/P6JHdl/SS7o7sfrKqbquq5FfJ/Lskrq+pMkndm89X12cKE/f2+JF+a5JdroLeunJYJ+5spmrDP70ryZFU9lOTuJD+44a8gTGjC/n5XkndU1e8luS3JtQO/CNuRqrotyceS/M2qOltV11XV91TV94yanM56wHkmyc8m+Rd7VCqL5d9nfdTqR0a/+z+QJFX116vqdLL5z/teFbzXquofjNZG+8Ykd1bVXaP9f9VnWV/v5bdG73//Lcmd3f1f9qbivTdJnznPXuA9Sd5aVX+Y5C2j7VTValU9d9en1yZZG51ndyd5T3cPJhDyeXL7Juyz76+qB0fn1fdn4EtczPv1V7m2BgAAABiWhR0hBAAAAMCLIxACAAAAGBiBEAAAAMDACIQAAAAABkYgBAAAADAwAiEAAACAgREIAQAAAAzM/weAiQpDQn96nQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func2(xi):\n",
    "    return 3 * xi - 2\n",
    "\n",
    "\n",
    "def denc2(y):\n",
    "    return  np.ones((len(y))) / 3 \n",
    "\n",
    "fig, axs = plt.subplots(1,2, figsize=(20,5))\n",
    "xi = uniform(loc=0, scale=1)\n",
    "\n",
    "xi_rvs = xi.rvs(size=10000)\n",
    "x1 = np.arange(0, 1.1, 0.1)\n",
    "axs[0].hist(xi_rvs, normed=True, bins=50)\n",
    "axs[0].plot(x1, xi.pdf(x1), 'r', lw=3)\n",
    "\n",
    "axs[1].hist(func2(xi_rvs), normed=True, bins=50, color='c')\n",
    "axs[1].plot(x1, xi.pdf(x1), 'r', lw=3)\n",
    "x2 = np.arange(-2, 1.1, 0.1)\n",
    "axs[1].plot(x2, denc2(x2), 'b', lw=4)\n",
    "axs[1].set_ylim(0, 1.1)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Модуль від лінійного перетворення"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Згенеруйте $n = 10000$ значень випадкової величини $\\xi$;\n",
    "2. Реалізуйте 2 сабплоти в одному рядку;\n",
    "3. На першому сабплоті намалюйте:\n",
    "   - нормовану гістограму згенерованих $n = 10000$ значень випадкової величини $\\xi$;\n",
    "   - функцію щільності випадкової величини $\\xi$;\n",
    "4. Отримайте $n = 10000$ значень випадкової величини $\\eta = |2 \\xi - 1|$ (застосуйте функцію модуль до згенерованих $n = 10000$ значень випадкової величини $\\xi$);\n",
    "5. На другому сабплоті намалюйте:\n",
    "   - нормовану гістограму отриманих $n = 10000$ значень випадкової величини $\\eta$;\n",
    "   - функцію щільності випадкової величини $\\xi$;\n",
    "   - функцію щільності випадкової величини $\\eta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func2(xi):\n",
    "    return abs(2 * xi - 1)\n",
    "\n",
    "\n",
    "def denc2(y):\n",
    "    return  np.ones((len(y)))\n",
    "\n",
    "fig, axs = plt.subplots(1,2, figsize=(20,5))\n",
    "xi = uniform(loc=0, scale=1)\n",
    "\n",
    "xi_rvs = xi.rvs(size=10000)\n",
    "x1 = np.arange(0, 1.1, 0.1)\n",
    "axs[0].hist(xi_rvs, normed=True, bins=50)\n",
    "axs[0].plot(x1, xi.pdf(x1), 'r', lw=3)\n",
    "\n",
    "axs[1].hist(func2(xi_rvs), normed=True, bins=50, color='c')\n",
    "axs[1].plot(x1, xi.pdf(x1), 'r', lw=3)\n",
    "x2 = np.arange(0, 1.1, 0.1)\n",
    "axs[1].plot(x2, denc2(x2), 'b', lw=4)\n",
    "axs[1].set_ylim(0, 1.2)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 Логарифм"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Згенеруйте $n = 10000$ значень випадкової величини $\\xi$;\n",
    "2. Реалізуйте 2 сабплоти в одному рядку;\n",
    "3. На першому сабплоті намалюйте:\n",
    "   - нормовану гістограму згенерованих $n = 10000$ значень випадкової величини $\\xi$;\n",
    "   - функцію щільності випадкової величини $\\xi$;\n",
    "4. Отримайте $n = 10000$ значень випадкової величини $\\eta = - \\log \\xi$ (застосуйте функцію модуль до згенерованих $n = 10000$ значень випадкової величини $\\xi$);\n",
    "5. На другому сабплоті намалюйте:\n",
    "   - нормовану гістограму отриманих $n = 10000$ значень випадкової величини $\\eta$;\n",
    "   - функцію щільності випадкової величини $\\xi$;\n",
    "   - функцію щільності випадкової величини $\\eta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JUrUyEJIkSVLViIArryzumz4dfvSjfOqRJKlaNeVdgCRJktRZTJmy6QHv2Af+tOP6zS98AU46CUaM6Nm6JEmqFc4QkiRJUvX5t+cYNKh9c8kSF5iWJGlzGAhJkiSp+mzXwhe/WNx17bUwdWo+5UiSVG0MhCRJklSVzj0X9t67fTulbIHptrb8apIkqVoYCEmSJKkqNTfDpEnFffffDz/9aT71SJJUTQyEJEmSVLWOPRYmTizuu+ACWLo0n3okSaoWBkKSJEmqat/+NvTt2749bx5ceml+9UiSVA0MhCRJklTVdt8dPvOZ4r5Jk+DJJ/OpR5KkamAgJEmSpKp30UWw667t262t2aLTKeVXkyRJvVlT3gVIkiRJWyKmTCnu+PgI+PK+6zf/9Cdo+OrjpC/sV9nCJEmqAs4QkiRJUm04cgEctLi47wd7sHJlPuVIktSbGQhJkiSpNgRwzrPQ0OE6sVf6841v5FaRJEm9loGQJEmSasduK+C9c4u6Lr8cnn8+n3IkSeqtDIQkSZJUW059Hoa2rN9ctQrOPNMFpiVJ6shASJIkSbVlUCv863NFXX/4A/z3f+dUjyRJvZCBkCRJkmrPca/AAUuKus47D+bNy6keSZJ6GQMhSZIk1Z4G4NNPQ5+29V2LFsE55+RXkiRJvYmBkCRJkmrTrivhY7OKun75S7j11pzqkSSpFzEQkiRJUu365zkcckhx15lnwuLF+ZQjSVJvYSAkSZKk2tWYuO46aGpq73rlFTj//PxKkiSpNzAQkiRJUk078EC46KLivhtugLvuyqceSZJ6AwMhSZIk1bzPfQ7GjCnuO+MMWL48n3okScqbgZAkSZJqXt++cN11ENHe98ILcPHF+dUkSVKeDIQkSZJUFw4/HM47r7jv+9+H++7Lpx5JkvJkICRJkqS68dWvwu67t2+nBKedBqtW5VeTJEl5MBCSJElS3RgwAK69trjv6afhy1/Opx5JkvJiICRJktRLRcSxEfF0RMyMiAs3MuafI+KJiJgRET+vdI3V6Kij4PTTi/u++U14+OF86pEkKQ9NeRcgSZKkDUVEI3AV8A5gDvBgRExOKT3RYcxewEXAW1NKiyNi+3yq7d1iypQNOyc2wq3j4dW+AKxdC6eeCg88AP36VbQ8SZJyUdIMIT+dkiRJqrjxwMyU0nMppRbgJuCETmNOB65KKS0GSCnNr3CN1WvQWvjUM0Vd06fDhV2e6UqSVHu6nSHkp1OSJEm52AWY3WF7DnBYpzF7A0TEfUAjcElK6Y+VKa8GvHkhvOMV+NOO67smTYJJO06DwxdtMDxNmFDB4iRJ6lmlzBDy0ylJkqTeqQnYC5gAnAxcExFDOw+KiDMiYmpETF2wYEGFS+zl/uNZ2HFlcd839oFFffKpR5KkCiklEOrq06ldOo3ZG9g7Iu6LiPsj4tiuXsiTEUmSpJLNBXbtsD2y0NfRHGBySmlNSmkW8AxZQFQkpXR1SmlcSmnciBEjeqzgqjRoLXz+SWhI7X2Lm+HyN0FbfmVJktTTynWXsZI+nfJkRJIkqWQPAntFxG4R0Qx8EJjcacxtZOdfRMRwsg/pnqtkkTVh39fgo88X9z24Lfx6ZC7lSJJUCaUEQmX7dEqSJEmlSSm1AmcDdwJPAreklGZExFciYmJh2J3Awoh4Argb+ExKaWE+FVe5D78ABywp7rt6d3h2UD71SJLUw0oJhPx0SpIkKQcppTtSSnunlPZIKV1W6PtiSmly4XlKKX0qpTQmpbR/SummfCuuYo3AxU/CoDXtfa0NcOkYWFmuSfWSJPUe3f7v5qdTkiRJqgs7rIZPF9+KntkD4Ko986lHkqQe1O1t5yH7dAq4o1PfFzs8T8CnCk2SJEmqTkcugONfhjt2au+7fWc4dFFhPrwkSbXB+a+SJElSR2c/C7uuKO771huZPbvr4ZIkVSMDIUmSJKmj/m3w+SegqcN955f14SMfgbVr8ytLkqRyMhCSJEmSOtt7OZxefI+Ue+6Byy/PqR5JksrMQEiSJEnqyolzYNyioq4vfQn+8pec6pEkqYwMhCRJkqSuNAAXPQVDW9Z3rV0LJ54Ic+bkV5YkSeVgICRJkiRtzLYt8Nmnirrmz89CodWrc6pJkqQyMBCSJEmSNuXNi+Ajzxd1/f3vcM45+ZQjSVI5GAhJkiRJ3Tn1eY4/vrjrmmvg6qvzKUeSpK1lICRJkiR1pwF+9jPYc8/i7rPPhr/9LZ+SJEnaGgZCkiRJUgmGDoVbb4WBA9v71qyB978fXn45v7okSdoSBkKSJElSifbbD268sbjv5ZfhAx+AlpYuv0SSpF7JQEiSJEnaDCeeCBdcUNx3333wyU/mU48kSVvCQEiSJEnaTJddBu98Z3HfD34AN9yQTz2SJG0uAyFJkiRpMzU2wi9+AbvtVtz/iU/Agw/mU5MkSZvDQEiSJEnaAttumy0y3b9/e9/q1fC+98H8+fnVJUlSKZryLkCSJEmqVgceCNddBx/6UHvfnDmww9FL4VuPQd+2Lr8uTZhQmQIlSdoIZwhJkiRJW+Hkk+FTn+rUOWMIXPYmWJtLSZIkdcsZQpIkSVIJYsqUje88PmDKAfDwsPa+v4yAH+4JZ8/s8dokSdpczhCSJEmStlZjgi/PgNGvF/f/eiT8cmQ+NUmStAkGQpIkSVI5DGqFK6bB8NXF/T/cA+4ZkU9NkiRthIGQJEmSVC7br4avT4MBre19KbL1hKYPya8uSZI6MRCSJEmSymnP17PLxxo73GFsTQN8bj94cUB+dUmS1IGBkCRJklRu4xbDp58p7lvWBy7YHxY151OTJEkdGAhJkiRJPeHYV+DUWcV9r/SHi/Zn+fJ8SpIkaR0DIUmSJKmn/MsLcPzLxX3PDOakk6C1tesvkSSpEgyEJEmSpJ4SwCefgUMXFXXfcQeceSaklE9ZkiQZCEmSJEk9qSnBJTNgr2VF3ddcA+efbygkScpHU94FSJIkSTVvwFr4+nQ462CY129997e/Dd+e9wL866xsNlEnacKEytUoSaorzhCSJEmSKmG7FrhiGgxpKe7/+RvgJ2/IpyZJUt0yEJIkSZIq5Q0r4D8fg8Frivtv3A1+PiqfmiRJdclASJIkSaqkPV+Hb06DgZ1uM3bN7vDLkfnUJEmqOwZCkiRJUqW9cRl8Yxr07xQK/WBPuHXnfGqSJNUVAyFJkiQpD2Neg8unQ7+1xf3f3Rtu3ymfmiRJdcNASJIkScrLAUvhq9OhuVMo9K294c4d8qlJklQXDIQkSZJ6qYg4NiKejoiZEXHhJsa9PyJSRIyrZH0qk0OWwKUzoE9be18K+MY+3HxzfmVJkmpbSYGQJyOSJEmVFRGNwFXAccAY4OSIGNPFuMHAucDfK1uhymr8IrhkBjR2CIXagg9/GG66Kb+yJEm1q9tAyJMRSZKkXIwHZqaUnksptQA3ASd0Me5S4ApgVSWLUw94y0L4whPQkNZ3rV0LH/oQ/OhHOdYlSapJpcwQ8mREkiSp8nYBZnfYnlPoWy8iDgZ2TSndXsnC1IOOfBUufrIoFEoJPvEJ+PrXs+eSJJVDUwljujoZOazjgI4nIxHxmTLWJ0mSpC5ERANwJXBqCWPPAM4AGDVqVM8Wpq13zPzs8ev7wNr2z28vvhgufuxF+LfnINqHpwkTKlufJKkmbPWi0h1ORs4vYewZETE1IqYuWLBga99akiSpls0Fdu2wPbLQt85gYD9gSkQ8DxwOTO5qLceU0tUppXEppXEjRozowZJVNsfMh0sf3/DuYzePgv98I6zt+sskSSpVKYGQJyOSJEmV9yCwV0TsFhHNwAeByet2ppSWppSGp5RGp5RGA/cDE1NKU/MpV2X35kXwzWkwsLW4/46d4NIx0BJdf50kSSUoJRDyZESSJKnCUkqtwNnAncCTwC0ppRkR8ZWImJhvdaqYA5bClY/C0Jbi/nu2h8/tDyu3esK/JKlOdbuGUEqpNSLWnYw0AtevOxkBpqaUJm/6FSRJkrQlUkp3AHd06vviRsZOqERNysHey2HSI/CZA2F+v/b+qdvCZw5k8eEwbFh+5UmSqlNJHymklO5IKe2dUtojpXRZoe+LXYVBKaUJzg6SJEmSymjUSvjuI7DriuL+GUM48kh4+eV8ypIkVS/nmEqSJEnVYIfV2UyhvZYVdU+fDm9+Mzz+eE51SZKqkoGQJEmSVC2GrcnWFDpgSVH3Cy/AW94Cd9yxka+TJKkTAyFJkiSpmgxaC9+YBocvLOpetgz+6Z9g0iRIKafaJElVw0BIkiRJqjZ92+DSx2Hi3KLutjY47zxoeM9c4n/uIaZMWd8kSerIQEiSJEmqRk0JznsWznkWGjpNCZq8C1xwACzr9qbCkqQ6ZSAkSZIkVasA3jcXvjYdBrQW73t4GJx1MMztn0tpkqTezUBIkiRJqnaHLYLvPwI7rCrunz0AzjwYHh2ST12SpF7LQEiSJEmqBbu9Dj98CPZdWtz/Wh/4zIHccEM+ZUmSeicvKpYkSZJqxbA1cOVj8M03wv/s0N7f2sDHPw4f/81LcM5MaG7r8svThAmVqVOSlDtnCEmSJEm1pLkNLn4SPj5rw32/3xnOPgjm9qt8XZKkXsVASJIkSao1AXzkBfjiDGheW7zv2cHwb+Pg3uG5lCZJ6h0MhCRJkqRaddQCuOoR2Hllcf/rTfCF/eCHe0Br5FObJClXBkKSJElSLdtzOfzXVHjbgg333bIrfHIsLGiufF2SpFwZCEmSJEm1btBa+PIMOGsmNHZaUPrxIXD6OJg6LJ/aJEm5MBCSJEmS6kEAJ86BSY/CiFXF+5Y2w2cP4JJLYO3arr5YklRrDIQkSZKkerLva3DNQ3DoouL+FHz5y3D00TCrixuUSZJqi4GQJEmSVG+GrIHLp8HHZkGkol1//jMccABcfz2ktJGvlyRVPQMhSZIkqR41AP/yAnzzMRjWUrRr+XI47TR4z3tg3rx8ypMk9SwDIUmSJKmeHbIErp664SVkwOTJsP/+cNttOdQlSepRBkKSJElSvRveAldM4wc/gAEDinctWADvfS+ceiosXZpLdZKkHmAgJEmSJAkCPvEJePRROPzwDXf/+MfZ2kJ331350iRJ5WcgJEmSJAmAmDKFvedO4f6v3gOnPQeNbUX7X3wxuwvZuefCsmU5FSlJKgsDIUmSJEnFGhOc8iL88GEY/foGu7/7XRgzBn772xxqkySVRVPeBUiSJEnqpfZaDv/1EFy3G/xyJKRYv2vOnOwuZByxAM6ZCduvLvrSNGFCZWuVJG0WZwhJkiRJ2rjmNvjE/4MrH4UdV264/94RcOqh8KuRsDY23C9J6pUMhCRJkiR1b+xSuOFBOPlFaEjF+1Y2wVV7wicOhqcH51OfJGmzeMmYJEmSpNL0a4MznoNj5sGVe8MTQ4r3PzsYzjwY3jOXeP0vMHDtJl/Oy8okKT/OEJIkSZK0efZ4Hb73CHzyaRjYWryvLeA3I+HU8XDXDtDW9UtIkvJlICRJkiRp8zUAE1+GnzwAR8/bcP+rfeHrb4KzDobpQzbcL0nKlYGQJEmSpC23bQt84Um4Yhrs1MWi009tA/9xEFwyBl7uV/n6JEldMhCSJEmStPXGL4LrH4QPvQB9urhO7J7t4aPj4b92h+WNla9PklTEQEiSJElSefRrg9NnwY0PwJHzN9y/pgFuGgUfOQwm70xr64ZDJEmVYSAkSZIkqbx2XgWXPAGTHoE3vrbh/iXN8O29GTsWfvc7SGnDIZKknmUgJEmSJKlnHLAUfvAwXPQkDF+9we4ZM2DiRDj8cLjzToMhSaokAyFJkiRJPacBeOc8+Mnf4dRZ0G/tBkMeeACOPRbe9ja4++7KlyhJ9chASJIkSVLP698GH30hC4be9UqXQ+67D44+Omv33lvh+iSpzpQUCEXEsRHxdETMjIgLu9j/qYh4IiKmRcT/RsQbyl+qJElSffEcTDVpRAtc+BRc+yDveU/XQ+6+O5st9K53ZbOHJEnl120gFBGNwFXAccAY4OSIGNNp2CPAuJTSAcCvgG+Uu1BJkqR64jmYat4er3PrrTB1Khx/fNdD7roLDjsM3v1u+MtfXGNIksqplBlC44GZKaXnUkotwE3ACR0HpJTuTilsB4WWAAATyUlEQVStKGzeD4wsb5mSJEl1x3Mw1YVDDoHbb4e//hX+4R+6HnPHHfD2t8Nb3gK33gptbZWtUZJqUSmB0C7A7A7bcwp9G3Ma8IetKUqSJEmeg6m+vPnN8Kc/wT33ZOFPV+6/H973PnjTm+Daa2H1hjcukySVqKmcLxYRpwDjgCM3sv8M4AyAUaNGlfOtJUmS6pbnYKpWMWVK1zsuAR4eCjfsBjOGbLD7mWfg9NPh9AtWw/vnwsSXSP94RE+WKkk1p5QZQnOBXTtsjyz0FYmIfwA+B0xMKXWZ1aeUrk4pjUspjRsxYsSW1CtJklQvPAdT/QrgkCXwvUfgO4/AYQu7HreoL1yzO5x0OJ/+NDz/fCWLlKTqVkog9CCwV0TsFhHNwAeByR0HRMRBwH+RnYjML3+ZkiRJdcdzMCmAA5fC5dPhugfhHa9AYxcLCK1o4lvfgt13h4kT4c47XWdIkrrTbSCUUmoFzgbuBJ4EbkkpzYiIr0TExMKwbwKDgF9GxKMRMXkjLydJkqQSeA4mdbL763DxU/Czv8OJs6Hf2g2GpAS/+x0ceyzssw98+9uweHEOtUpSFYiU070bx40bl6ZOndojrz36wtt75HUlSao1z1/+7h577Yh4KKU0rsfeQFukJ8/BNroejNQTXmuCyTvDr0fCkuaNDuvfH045Bc46Cw48sIL1SVJOSj0HK+WSMUmSJEnqXbZphVNehJvuh08/zdixXQ9buRKuuQbGjoUjjoCf/hRWrKhsqZLUGxkISZIkSapefdvg3S/z8MNw771w8snQp0/XQ++7D/7lX2DHHbO7lP31r9llZpJUjwyEJEmSJFW9CHjrW+HnP4fZs+HSS2HkyK7HLlsG116bjX/Tm+Dyy2HuBvfwk6TaZiAkSZIkqabssAN8/vMwaxb8+tdw9NEbH/v003DRRTBqFBx3HNxyC6xeXblaJSkvTXkXIEmSJEk9oakJ3ve+rD35JFx/fbaG0Lx5G45ta4M//jFrDFoDb3sVjp4PBy2Bxg2vK0sTJvR4/ZLUkwyEJEmSJFW9Uu5yl745ga99De68E264IbtF/Zo1XQxc3gf+sFPWhrbA2xdk4dD+S73GQlLNMBCSJEmSVBfWh0aDgHOAj/SB/9ke/rgT/L9BXX/RkmaYvEvWhq+GCfPh6PmkI7N1iySpWplvS5IkSapPQ9fAiXPh2qlw9VR47xwY0rLx8a/2hV/tCmcewh57wPnnw5//DGvXVq5kSSoXAyFJkiRJ2ms5/MdM+NXf4IrH4NiXYWDrRofPmgVXXglHHpndxv5jH4PbboMVKypYsyRtBQMhSZIkSVqnKcH4xXDB0/Cb++Cy6XDMPOi38WlAr74KN94I730vDB8OJ5yQLWC9YEHlypakzeUaQpIkSZLUleYEb1mYtVUNcP92cPf2cP+20NLY5ZesXAmTJ2ctAtKYpXDoIhi/CPZeBl18mXcsk5QHAyFJkiRJ6k6/NpiwIGsrGvnlirfx29/C7bfD4sVdf0lKwIwhWbtxN9hmDYwrhEOHLoZtN7FekST1MAMhSZIkSdocA9Zy4vFw4onZbev/8hf47W+zNYRefHETX/daH/i/HbIGsOcyGL+IKcCb3wx9+1agdkkqcA0hSZIkSdpCffrA0UfDpEnw/PPwyCNwySUwdmwJXzxzMPz8DRx1FAwdCsccA1/9Ktx3H7Q4eUhSD3OGkCRJkiSVQUQWBI0dC1/6EsyZA7t+9yl4YFt4aBgs77PRr121Cv7v/7IGMGAAHHEEHHVU1g45BJr87U1SGflPiiRJkiRtppgypbSBxwPHvwJrA54cnIVDD24LTw+GFBv9shUr4K67sgYweHB2Wdlb35q1ww6DQYO2+tuQVMcMhCRJkiSppzUm2O+1rH38eVjaB6YOgwe2ZeQTOzJnzqa/fNmy4oCIhgR7LIf9lmavue9S2GG1dyyTVDIDIUmSJEmqtCFr4Jj5cMx85qSn4KX+8MhQeLTQFnazwnRbwLODs3ZroW/EKk46Cg49NGuHHOIsIkkbZyAkSZIkSXkKYJeVWfvHlyEBs/vDo8PaQ6Ilzd2/zoJ+3HIL3HJL4WUDxoxpD4gOPRQOOMC7mUnKGAhJkiRJUm8SwKiVWZv4UiEgGgDTt4EZQ+DxIdl2N1KCGTOyduONWV9zMxx4IBx0UPsC2Pvv70wiqR4ZCEmSJElSbxbAqBVZe/crWd/SPvD4Nlk4NGMbeGobWNPQ7Uu1tMCDD2Zt/csH7LVXcUg0dizsuGPPfDuSegcDIUmSJEmqNkPWwFsXZg2gJWDmYCa1Hrw+8Hn66dJeKiV45pms3Xxze/+IEbDvvrDfflnbd9+sDRtW/m9HUuUZCEmSJElStWtOMOY1/mNCe9fSpfDQQ1k49MAD2ePs2aW/5IIFMGVK1jraeefikOiNb8za8OFl+D4kVYyBkCRJkiTVoCFD4Oijs7bOvHmw44+nwbODYOYg+H+DYE5/SFHy6770Utbuuqu4f7vt2sOhffZpf77HHtCnT5m+KUllYyAkSZIkSTUiOk/n6cp4YPyi9u2VjfDcwCwgerYQEj03EFoaN+u9Fy6Ev/41ax01NcHo0VkwtOeeWVv3fLfdoF+/zXobSWViICRJkiRJ9az/Wtj3taytsxZ4uT88PxBmDYTnB2SPswdAa/eLV3fU2gozZ2btzjuL90XAyJFZOHT3gJdgx1WwwyrYaVX2fNsW6PB2acKELf42JRUzEJIkSZIkFWsERq7M2hGvtve3RnaJ2bqg6MUBWZvTf7NnFEG2oPXs2evWNtp5wwF92rKAaMesff1vsOuuMGpU9rjLLtDcvKXfpFTfDIQkSZIkSaVpSjB6RdYmLGjvbwPm94MX+2eziF4ckD3OHgCv9t3y91vTAHMGZA24+Ped9keCYS2w/epCWwUjVnPzhD3ZeecsMNppJy9Lk7piICRJkiRJ2joNrJ/Fw/jFxftWNsLcfvBSf5hbaC8V2vy+m7Wg9QZSwKK+WXuqvfukHxYP23bbLBxaFxLtvHPWdtyxve2wAwwYsOWlSNXGQEiSJEmS1HP6r4U9X89aZy0N8HK/LCR6pd+GbVl5bk+2aFHWpk/f9LjBg4tDoh13hO+9PguGtMCwNTC0BYauyZ4PbIVCluXaRqpGBkKSJEmSpHw0t8EbVmStK8sbYV6/LDR6pV/2fEHf9sdFzVs3w6iTZcuy9uyzHXt363pwU1sWDg1t4R2jYfjwrG23XfHjuufbbZfNQIrylSttFQMhSZIkSVLvNGgtDHod9uhidhHAmoCFfWFe3+zyswX9ssdX+8LC5uxxUTO09UAK09qQvf6rffmfmaV9Sd++MGxYdglbx9axb9gwGDp0w9avn2GSystASJIkSZJUnfqk9rWLNmYtsKQQDr3anAVI6x4X98kCo3VtbcPGX6cMVq+GV17J2mZraoNBrTColUN3GsA228CQIWzycfDg9sd1zbuyaR0DIUmSJElS7WoEtmvJ2hs3Ma4NWNZUHBAtbs7CpCV9sra4GZYWHlc1VugbKGhtKNTSzINztvxlmps3DIoGDYKBA7PHjq1j38CB2SVvAwe2t47bTaYLVcc/MkmSJEmSGoAhrVnbbSNrGnW0qqEQFBVCoqV94LV1j02dtguPa3p2BlIpWlpg4cKslVNzcxYQrWv9+3e93b9/cevXb+Pb/fplrW/f9ucd+xryP5xVzUBIkiRJkqTN1a8NdlydtVIkYHVDdue0ZU1ZaLSsEB4t79O+vbyp69YLwqRNaWnJ2pIlFXzTPm0dWsoWKe/TVvT4rh2G0dycBUilPHZsffpsvK9Pn/bWcXvd86am7LGxsfeu/VRSIBQRxwKTyCbbXZtSurzT/r7AT4BDgIXASSml58tbqiRJUn3xHEySakiQhUj9VsOIEkOkjloaigOi1xvh9Q6PKwrPl3d4vqIJVjTCysbscUVTzyywnZc1Dd0GZXdWqJRN6RgerQuK1rU//hH22iufuroNhCKiEbgKeAcwB3gwIianlJ7oMOw0YHFKac+I+CBwBXBSTxQsSZJUDzwHkyQVaW6DbVuytqUSWbC0ohAQrWzKwqJNtVUNWZC0uqGw3Zg9X9Vh/6pGSDUUNJXZmjVZ60pbW2Vr6aiUGULjgZkppecAIuIm4ASg48nICcAlhee/Ar4fEZFSSmWsVZIkqZ54DiZJKq8A+rZlbdhGEootkchm6qxqgNXrAqPC81UN0NLYabvQ1o1d3UVfS4e2ptN2S/czg6pFnz75vXcpgdAuwOwO23OAwzY2JqXUGhFLge2AV8tRpCRJUh3yHEySVB2CbAZTcxvQWpn3bCO781pLtAdE61pLbLjd2sXzNR3GtUbW1j1f39d5u/B8bcfHwrjOz9dGt5fo9fZAqGwi4gzgjMLm8oh4uofeajieCFWSx7vyPOaV5fGuLI93BcUVPXq839BDr6vN5DlYzfO458Pjng+Pez487j1k1Khuh2zJsS/pHKyUQGgusGuH7ZGFvq7GzImIJmAI2cKGRVJKVwNXl1LY1oiIqSmlcT39Psp4vCvPY15ZHu/K8nhXlse7V/McTCXxuOfD454Pj3s+PO756cljX8pFdw8Ce0XEbhHRDHwQmNxpzGTgo4XnJwL/57XrkiRJW8VzMEmS1GO6nSFUuB79bLK7tTUC16eUZkTEV4CpKaXJwHXATyNiJrCI7IRFkiRJW8hzMEmS1JNKWkMopXQHcEenvi92eL4K+EB5S9sqPT4lWkU83pXnMa8sj3dlebwry+Pdi3kOphJ53PPhcc+Hxz0fHvf89NixD2cVS5IkSZIk1ZdS1hCSJEmSJElSDanqQCgijo2IpyNiZkRc2MX+vhFxc2H/3yNidOWrrB0lHO9PRcQTETEtIv43Irzd8Fbo7nh3GPf+iEgR4ar/W6mUYx4R/1z4OZ8RET+vdI21pIR/U0ZFxN0R8Ujh35Xj86izVkTE9RExPyIe38j+iIjvFv48pkXEwZWuUdWr1P+zVF7d/b1Wz4iIXQv/P607Hzg375rqQUT0i4gHIuKxwnH/ct411ZOIaCyck/0+71rqRUQ8HxHTI+LRiJjaE+9RtYFQRDQCVwHHAWOAkyNiTKdhpwGLU0p7At8GrqhslbWjxOP9CDAupXQA8CvgG5WtsnaUeLyJiMHAucDfK1th7SnlmEfEXsBFwFtTSvsC51W80BpR4s/454FbUkoHkS2U+4PKVllzbgSO3cT+44C9Cu0M4IcVqEk1oNT/s9QjbmTTf6/VM1qB81NKY4DDgbP8ma+I1cDRKaUDgbHAsRFxeM411ZNzgSfzLqIOHZVSGpvnbed7q/HAzJTScymlFuAm4IROY04Aflx4/ivgmIiICtZYS7o93imlu1NKKwqb9wMjK1xjLSnl5xvgUrKgc1Uli6tRpRzz04GrUkqLAVJK8ytcYy0p5XgnYJvC8yHASxWsr+aklP5MdheqjTkB+EnK3A8MjYidKlOdqlyp/2epzEr4e60ekFJ6OaX0cOH5MrJfknfJt6raV/j/aXlhs0+huSBuBUTESODdwLV516LyquZAaBdgdoftOWz4D/H6MSmlVmApsF1Fqqs9pRzvjk4D/tCjFdW2bo934XKOXVNKt1eysBpWys/43sDeEXFfRNwfEX4qu+VKOd6XAKdExByyuyydU5nS6tbm/jsvrePPjupWYUmKg3C2dkUULlt6FJgP/Cml5HGvjO8AnwXa8i6kziTgroh4KCLO6Ik3qOZASL1URJwCjAO+mXcttSoiGoArgfPzrqXONJFdTjMBOBm4JiKG5lpRbTsZuDGlNBI4Hvhp4WdfkqTcRcQg4NfAeSml1/Kupx6klNamlMaSXYkwPiL2y7umWhcR/wjMTyk9lHctdeiIlNLBZJdknxURby/3G1TzifVcYNcO2yMLfV2OiYgmsksOFlakutpTyvEmIv4B+BwwMaW0ukK11aLujvdgYD9gSkQ8T3b9+mQXlt4qpfyMzwEmp5TWpJRmAc+QBUTafKUc79OAWwBSSn8D+gHDK1JdfSrp33mpC/7sqO5ERB+yMOhnKaXf5F1PvUkpLQHuxjW0KuGtwMTC7xw3AUdHxH/nW1J9SCnNLTzOB24lu0S7rKo5EHoQ2CsidouIZrIFRyd3GjMZ+Gjh+YnA/6WUvM50y3R7vCPiIOC/yMIg11bZOps83imlpSml4Sml0Sml0WRrNk1MKfXI6vN1opR/U24jmx1ERAwnu4TsuUoWWUNKOd4vAscARMSbyAKhBRWtsr5MBv6lcLexw4GlKaWX8y5KVaGUv89SzSisSXod8GRK6cq866kXETFi3czsiOgPvAN4Kt+qal9K6aKU0sjC7xwfJPud+pScy6p5ETGwcAMhImIg8E6g7HeUbCr3C1ZKSqk1Is4G7gQagetTSjMi4ivA1JTSZLJ/qH8aETPJFtz7YH4VV7cSj/c3gUHALwtrd7+YUpqYW9FVrMTjrTIq8ZjfCbwzIp4A1gKfSSk563ALlHi8zye7LO+TZNdQn2qov+Ui4hdkgebwwrpMXyJbkJOU0o/I1mk6HpgJrAA+lk+lqjYb+/ucc1l1oau/1yml6/Ktqi68FfgIML2wng3AxSmlO3KsqR7sBPy4cGfDBrI7kXoLdNWqHYBbC79XNwE/Tyn9sdxvEp5bS5IkSZIk1ZdqvmRMkiRJkiRJW8BASJIkSZIkqc4YCEmSJEmSJNUZAyFJkiRJkqQ6YyAkSZIkSZJUZwyEJEmSJEmS6oyBkCRJkiRJUp0xEJIkSZIkSaoz/x+7TgYsxUc35wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func2(xi):\n",
    "    return -np.log(xi)\n",
    "\n",
    "\n",
    "def denc2(y):\n",
    "    return  np.exp(-y)\n",
    "\n",
    "fig, axs = plt.subplots(1,2, figsize=(20,5))\n",
    "xi = uniform(loc=0, scale=1)\n",
    "\n",
    "xi_rvs = xi.rvs(size=10000)\n",
    "x1 = np.arange(0, 1.1, 0.1)\n",
    "axs[0].hist(xi_rvs, normed=True, bins=50)\n",
    "axs[0].plot(x1, xi.pdf(x1), 'r', lw=3)\n",
    "\n",
    "x2 = np.arange(0, 5, 0.1)\n",
    "axs[1].hist(func2(xi_rvs), normed=True, bins=x2, color='c')\n",
    "axs[1].plot(x1, xi.pdf(x1), 'r', lw=3)\n",
    "axs[1].plot(x2, denc2(x2), 'b', lw=4)\n",
    "axs[1].set_ylim(0, 1.2)\n",
    "\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 Одиничний квадрат"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Реалізуйте випадкову величину рівномірно розподілену на одиничному квадраті.\n",
    "Тобто $\\xi = (x, y), \\quad x, y \\sim Unif(0, 1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "xi = uniform(loc=0, scale=1)\n",
    "\n",
    "n = 10 ** 5\n",
    "xi1_rvs = xi.rvs(size=n)\n",
    "xi2_rvs = xi.rvs(size=n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Знайдіть функцію щільності випадкової величини $\\xi_1 = x^2 + y^2$.\n",
    "Намалюйте її разом із нормованою гістограмою $n = 100000$ значень випадкової величини $\\xi_1$,\n",
    "отриманою перетвореннями випадкових величин $x, y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func1(x, y):\n",
    "    return x ** 2 + y ** 2\n",
    "    \n",
    "    \n",
    "def denc1(vect):\n",
    "    return 0.5 / np.sqrt(vect)\n",
    "    \n",
    "    \n",
    "fig, axs = plt.subplots(1, 1, figsize=(20,5))\n",
    "axs.hist(func1(xi1_rvs, xi2_rvs), normed=True, bins=150)\n",
    "x2 = np.arange(0.005, 1.005, 0.01)\n",
    "# axs.plot(x, x / x, 1 + x, denc1(x + 1) color='r', lw=4)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Знайдіть функцію щільності випадкової величини $\\xi_2 = \\max (x, y)$.\n",
    "Намалюйте її разом із нормованою гістограмою $n = 100000$ значень випадкової величини $\\xi_2$,\n",
    "отриманою перетвореннями випадкових величин $x, y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func2(x, y):\n",
    "    return np.maximum(x, y)\n",
    "    \n",
    "\n",
    "def dens2(x):\n",
    "    return 2 * x\n",
    "    \n",
    "fig, axs = plt.subplots(1, 1, figsize=(20,5))\n",
    "axs.hist(func2(xi1_rvs, xi2_rvs), normed=True, bins=100)\n",
    "x = np.arange(0, 1.02, 0.02)\n",
    "axs.plot(x, dens2(x), color='r', lw=4)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Знайдіть функцію щільності випадкової величини $\\xi_3 = |x - y|$.\n",
    "Намалюйте її разом із нормованою гістограмою $n = 100000$ значень випадкової величини $\\xi_3$,\n",
    "отриманою перетвореннями випадкових величин $x, y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func3(x, y):\n",
    "    return abs(x - y)\n",
    "    \n",
    "    \n",
    "def dens3(x):\n",
    "    return 2 * (1 - x)\n",
    "\n",
    " \n",
    "fig, axs = plt.subplots(1, 1, figsize=(20,5))\n",
    "axs.hist(func3(xi1_rvs, xi2_rvs), normed=True, bins=100)\n",
    "x = np.arange(0, 1.02, 0.02)\n",
    "axs.plot(x, dens3(x), color='r', lw=4)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}