{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/800x800-04.jpg\" height=\"200\" width=\"300\"> \n",
    "\n",
    "# <center> R для тервера и матстата. <br>  <br> Домашка номер раз! </center>\n",
    "\n",
    "Данный ноутбук является домашкой по курсу «R для теории вероятностей и математической статистики» (РАНХиГС, 2017-2018). Автор ноутбука [вот этот парень по имени Филипп.](https://vk.com/ppilif) Если у вас для него есть деньги, слава или женщины, он от этого всего не откажется. Ноутбук распространяется на условиях лицензии [Creative Commons Attribution-Share Alike 4.0.](https://creativecommons.org/licenses/by-sa/4.0/) При использовании обязательно упоминание автора курса и аффилиации. При наличии технической возможности необходимо также указать активную гиперссылку на [страницу курса.](https://fulyankin.github.io/R_probability/) На ней можно найти другие материалы. Фрагменты кода, включенные в этот notebook, публикуются как [общественное достояние.](https://creativecommons.org/publicdomain/zero/1.0/)\n",
    "\n",
    "----------------------\n",
    "\n",
    "Приветствую вас внутри первой домашки. У каждой домашки должны быть свои герои (но это неточно). Моими героями являетесь вы! Вы - герои не потому, что я хочу кого-то простебать или обидеть, а потому что я всех вас очень люблю и хочу увековечить. Кто-то называет именами любимых людей вновь открытые звёзды и острова, кто-то вновь созданный вордовский файл для нира, а кто-то делает их героями своих историй. Я не Джордж Мартин, в моих историях никто не погибнет. \n",
    "\n",
    "__Краткий брифинг:__\n",
    "\n",
    "* В тетрадке $ 10 $ задачек. Нужно решить любые пять.\n",
    "* Некоторые задачи можно решить вручную. За это баллы не ставятся, но можно попробовать.\n",
    "* Все решения выложу после дедлайна. \n",
    "* Дедлайн: следующая среда (25 апреля), утро. \n",
    "* Следующая пара начнётся с разбора домашки.\n",
    "\n",
    "Ближе к делу. С чего начинается любой скрипт? Правильно! С подгрузки пакетов :) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(\"ggplot2\")  # Пакет для красивых графиков \n",
    "library(\"grid\")     # Пакет для субплотов\n",
    "\n",
    "# Отрегулируем размер картинок, которые будут выдаваться в нашей тетрадке\n",
    "library('repr')\n",
    "options(repr.plot.width=4, repr.plot.height=3)\n",
    "\n",
    "# Внимание! Если вы делаете дз в Rstudio, то вам не нужны пакеты grid, repr и т.п.\n",
    "# Вам нужен только пакет ggplot2! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Полезные функции: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 2\n",
       "3. 2\n",
       "4. 2\n",
       "5. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2 2 2 2 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rep(2,5)  # повторяет число 2 целых 5 раз"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>0.2</li>\n",
       "\t<li>0.4</li>\n",
       "\t<li>0.6</li>\n",
       "\t<li>0.8</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 0.2\n",
       "\\item 0.4\n",
       "\\item 0.6\n",
       "\\item 0.8\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 0.2\n",
       "3. 0.4\n",
       "4. 0.6\n",
       "5. 0.8\n",
       "6. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.0 0.2 0.4 0.6 0.8 1.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seq(0,1,0.2)  # выдаёт все числа от 0 до 1 с шагом 0.2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>-1</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item -1\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. -1\n",
       "3. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  1 -1  2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- c(1,2,3)\n",
    "y <- c(2,-1,4)\n",
    "z <- c(3,5,2)\n",
    "\n",
    "pmin(x,y,z)   # находит поэлементные минимумы во всех векторах"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3"
      ],
      "text/latex": [
       "3"
      ],
      "text/markdown": [
       "3"
      ],
      "text/plain": [
       "[1] 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "which.max(x) # выдаёт позицию максимума"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задачка 1\n",
    "\n",
    "В R куча встроенных наборов данных. Например, в наборе данных `chickwts` лежат веса куриц и тип корма, который используется для их выращивания."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>weight</th><th scope=col>feed</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>179      </td><td>horsebean</td></tr>\n",
       "\t<tr><td>160      </td><td>horsebean</td></tr>\n",
       "\t<tr><td>136      </td><td>horsebean</td></tr>\n",
       "\t<tr><td>227      </td><td>horsebean</td></tr>\n",
       "\t<tr><td>217      </td><td>horsebean</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " weight & feed\\\\\n",
       "\\hline\n",
       "\t 179       & horsebean\\\\\n",
       "\t 160       & horsebean\\\\\n",
       "\t 136       & horsebean\\\\\n",
       "\t 227       & horsebean\\\\\n",
       "\t 217       & horsebean\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "weight | feed | \n",
       "|---|---|---|---|---|\n",
       "| 179       | horsebean | \n",
       "| 160       | horsebean | \n",
       "| 136       | horsebean | \n",
       "| 227       | horsebean | \n",
       "| 217       | horsebean | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  weight feed     \n",
       "1 179    horsebean\n",
       "2 160    horsebean\n",
       "3 136    horsebean\n",
       "4 227    horsebean\n",
       "5 217    horsebean"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(chickwts,5)  # команда head позволяет посмотреть на\n",
    "                  # первые пять строк таблички "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Постройте гистограмму с распределением веса куриц с 20 столбиками. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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6YiIwIIIIAAAuEJEIDDs6QkBBBAAAEE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\nQLso5hiT8AAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# легче лёгкого! \n",
    "qplot(chickwts$weight, bins=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Постройте эмпирическую функцию распределения для веса куриц. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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r16VbKysgLkZt7LRYsWVQu0423bqsFO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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# скопипастим код из лекции\n",
    "ggplot(chickwts, aes(x = weight))+   # на какой таблице строи график \n",
    "        stat_ecdf( )                 # какой именно график строим "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WwdpA0EQAAEQMC0BDAMybSmRcZAIH0E7DsdlPN6Ljm+cZK9QnzHfzcxlPeGegoe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\nDzxz/gqTQijkAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Можно сделать график чуть красивше! Розовым, пунктирным и большим! \n",
    "ggplot(chickwts, aes(x = weight))+\n",
    "        stat_ecdf(linetype = 'dashed', color = \"magenta\", size = 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Найдите базовые характеристики распределения:\n",
    "\n",
    "* средний вес курицы\n",
    "* медианный вес курицы\n",
    "* дисперсию веса куриц \n",
    "* среднее квадратическо отклонения веса куриц \n",
    "* эмпирические квантили уровня 5%, 50% и 95%. \n",
    "* правда ли, что 50% квантиль совпал с медианой? А почему?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "261.30985915493"
      ],
      "text/latex": [
       "261.30985915493"
      ],
      "text/markdown": [
       "261.30985915493"
      ],
      "text/plain": [
       "[1] 261.3099"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# сохраним вес курицы в отдельный вектор, чтобы было проще\n",
    "x <- chickwts$weight\n",
    "mean(x) # среднее"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "258"
      ],
      "text/latex": [
       "258"
      ],
      "text/markdown": [
       "258"
      ],
      "text/plain": [
       "[1] 258"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "median(x) # медиана"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "6095.50261569416"
      ],
      "text/latex": [
       "6095.50261569416"
      ],
      "text/markdown": [
       "6095.50261569416"
      ],
      "text/plain": [
       "[1] 6095.503"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var(x) # дисперсия"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "78.0736998975594"
      ],
      "text/latex": [
       "78.0736998975594"
      ],
      "text/markdown": [
       "78.0736998975594"
      ],
      "text/plain": [
       "[1] 78.0737"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sd(x) # стандартное отклонение (корень из дисперсии)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>5%</dt>\n",
       "\t\t<dd>140.5</dd>\n",
       "\t<dt>50%</dt>\n",
       "\t\t<dd>258</dd>\n",
       "\t<dt>95%</dt>\n",
       "\t\t<dd>385</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[5\\textbackslash{}\\%] 140.5\n",
       "\\item[50\\textbackslash{}\\%] 258\n",
       "\\item[95\\textbackslash{}\\%] 385\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "5%\n",
       ":   140.550%\n",
       ":   25895%\n",
       ":   385\n",
       "\n"
      ],
      "text/plain": [
       "   5%   50%   95% \n",
       "140.5 258.0 385.0 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q = c(0.05, 0.5, 0.95)\n",
    "quantile(x,q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "TRUE"
      ],
      "text/latex": [
       "TRUE"
      ],
      "text/markdown": [
       "TRUE"
      ],
      "text/plain": [
       "[1] TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# конечно правда! Медиана это и есть 50% квантиль\n",
    "median(x) == quantile(x, 0.5, names = FALSE)  # names отвечает за подписывание имён"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сделали упражнение? Ответили на вопросы? Вы офигенны! Вы уже можете больше, чем среднестатистический аудитор из большой четвёрки ;) Двигайтесь дальше в таком же темпе. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задачка 2 \n",
    "\n",
    "Случайные величины $X_1, \\ldots, X_5$ имеют равномерное распределение на отрезке $[0;1]$ и независимы. С помощью симуляций оцените:\n",
    "\n",
    "а) $P(\\min\\{X_1, \\ldots, X_5\\} > 0.2)$\n",
    "\n",
    "б) $P(\\min\\{X_1, \\ldots, X_5\\} > 0.2 \\mid X_1 + X_2 < 0.5)$\n",
    "\n",
    "в) $E(\\min\\{X_1, \\ldots, X_5\\})$\n",
    "\n",
    "г) $E(\\min\\{X_1, \\ldots, X_5\\} \\mid X_1 + X_2 < 0.5)$\n",
    "\n",
    "Насколько логично то, что вы получили? Попробуйте порассуждать на эту тему. Постройте гистограмму для распределения минимума из этих случайных величин гистограмму для распределения максимума из этих случайных величин. Вспомните как выглядит теоретическая плотность распределения максимума и теоретическая плотность распределения минимума. Мы ещё с ними столкнёмся ;) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PWrWKOjvbR+/XrbtGmT68HqV+dpp53m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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# немного осмысленной копипасты из лекции\n",
    "n_obs <- 10^6  # число наблюдений\n",
    "\n",
    "# пяток случайных величин\n",
    "x_1 <- runif(n_obs, min = 0, max = 1)\n",
    "x_2 <- runif(n_obs, min = 0, max = 1)\n",
    "x_3 <- runif(n_obs, min = 0, max = 1)\n",
    "x_4 <- runif(n_obs, min = 0, max = 1)\n",
    "x_5 <- runif(n_obs, min = 0, max = 1)\n",
    "\n",
    "# находим минимальное значение в каждой пятёрке чисел \n",
    "mn <- pmin(x_1, x_2, x_3, x_4, x_5)\n",
    "\n",
    "qplot(mn)  # посмотрим на гистограмму, интересно же! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.326883"
      ],
      "text/latex": [
       "0.326883"
      ],
      "text/markdown": [
       "0.326883"
      ],
      "text/plain": [
       "[1] 0.326883"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "success <- mn > 0.2     # TRUE будет стоять в тех местах, где это правда \n",
    "sum(success) / n_obs    # а вот и итоговая оценка вероятности! :) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0025"
      ],
      "text/latex": [
       "0.0025"
      ],
      "text/markdown": [
       "0.0025"
      ],
      "text/plain": [
       "[1] 0.0025"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# также легко решаем пункт b) \n",
    "\n",
    "uslovie = x_1 + x_2 < 0.5  # находим позиции, где выполнено условие \n",
    "\n",
    "success <- mn[uslovie] > 0.2  # делаем срез по этому условию \n",
    "sum(success) / n_obs          # наконец получаем оценку вероятности \n",
    "# Вполне логично, что она уменьшилась по сравнению с предыдущей, мы же наложили ограничения! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.166422290443591"
      ],
      "text/latex": [
       "0.166422290443591"
      ],
      "text/markdown": [
       "0.166422290443591"
      ],
      "text/plain": [
       "[1] 0.1664223"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# решаем пункт c) \n",
    "mean(mn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0690854509851776"
      ],
      "text/latex": [
       "0.0690854509851776"
      ],
      "text/markdown": [
       "0.0690854509851776"
      ],
      "text/plain": [
       "[1] 0.06908545"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# и также пункт d) \n",
    "# Вполне логично, что математическое ожидание меньше, у нас же ограничения! \n",
    "mean(mn[uslovie])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задачка 3\n",
    "\n",
    "Иван Фёдорович Крузенштерн (ШТО?!) случайным образом с возможностью повторов выбирает $10$ натуральных чисел от $1$ до $100$. Пусть $X$ — минимум из этих чисел, а $Y$ — максимум. С помощью симуляций оцените \n",
    "\n",
    "а) $ P(Y > 3X)$\n",
    "\n",
    "б) $E(X \\cdot Y)$\n",
    "\n",
    "в) $P(Y > 3X \\mid Y < X^2)$\n",
    "\n",
    "г) $E(X \\cdot Y \\mid Y < X^2)$\n",
    "\n",
    "д) $E \\left( \\frac{X}{X + 2Y} \\right)$\n",
    "\n",
    "е) $Corr(X,Y)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>51</li>\n",
       "\t<li>49</li>\n",
       "\t<li>90</li>\n",
       "\t<li>8</li>\n",
       "\t<li>61</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 51\n",
       "\\item 49\n",
       "\\item 90\n",
       "\\item 8\n",
       "\\item 61\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 51\n",
       "2. 49\n",
       "3. 90\n",
       "4. 8\n",
       "5. 61\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 51 49 90  8 61"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "8"
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      "text/latex": [
       "8"
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      "text/markdown": [
       "8"
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      "text/plain": [
       "[1] 8"
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     "metadata": {},
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    {
     "data": {
      "text/html": [
       "90"
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      "text/latex": [
       "90"
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      "text/markdown": [
       "90"
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      "text/plain": [
       "[1] 90"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Ивану Фёдоровичу грех не помочь!\n",
    "# Основная сложность этой задачи в генерации выборки, давайте попрубуем \n",
    "# разобраться пошагово и для начала сгенерируем только одну выборку\n",
    "\n",
    "natural <- sample(1:100, size = 5, replace = TRUE)\n",
    "\n",
    "natural\n",
    "\n",
    "min(natural)  # случайная величина X\n",
    "max(natural)  # случайная величина Y\n",
    "\n",
    "# нам таких выборок понадобится очень много, придётся написать цикл для их генерации..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.97192"
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      "text/latex": [
       "0.97192"
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      "text/markdown": [
       "0.97192"
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      "text/plain": [
       "[1] 0.97192"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^6\n",
    "x = rep(0, n_obs)   # создаём два вектора из нулей, так будет быстрее работать \n",
    "y = rep(0, n_obs)   # чем ежели создавать пустой вектор (почему объясню на паре)\n",
    "                    # в вектор x будем записывать минимумы, в y максимумы\n",
    "for(i in 1:n_obs){\n",
    "    natural = sample(1:100, size = 10, replace = TRUE)  # сгенерировали выборку\n",
    "    x[i] = min(natural)                                 # нашли минимум и максимум для неё\n",
    "    y[i] = max(natural)\n",
    "}\n",
    "\n",
    "# Вот и вся генерация, осталось только ответить на вопросы задачи\n",
    "# a)\n",
    "\n",
    "success = y > 3*x\n",
    "sum(success) / n_obs  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "885.238837"
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      "text/latex": [
       "885.238837"
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      "text/markdown": [
       "885.238837"
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      "text/plain": [
       "[1] 885.2388"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# б) \n",
    "mean(x*y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.363526"
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      "text/latex": [
       "0.363526"
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      "text/markdown": [
       "0.363526"
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      "text/plain": [
       "[1] 0.363526"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# в) \n",
    "usl = y < x^2\n",
    "\n",
    "success <- y[usl] > 3*x[usl]\n",
    "sum(success) / n_obs  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1638.87316333253"
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      "text/latex": [
       "1638.87316333253"
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      "text/markdown": [
       "1638.87316333253"
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      "text/plain": [
       "[1] 1638.873"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# г) \n",
    "mean(x[usl]*y[usl])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0483075197452732"
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      "text/latex": [
       "0.0483075197452732"
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      "text/markdown": [
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      "text/plain": [
       "[1] 0.04830752"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# д)\n",
    "z = x/(x + 2*y)\n",
    "mean(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.100989209250183"
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      "text/latex": [
       "0.100989209250183"
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       "[1] 0.1009892"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# e)\n",
    "cor(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задачка 4\n",
    "\n",
    "Миша поступил на первый курс экономического факультета, потому что у него в крови всегда была предпренимательская жилка. На первом курсе она довела его, и он решил учёбу забросить и стать комерсом. На паблике \"Бизнес-молодость\" Миша подсмотрел шикарную бизнес-модель и решил, что будет торговать еженедельными газетами. На первом курсе Миша прослушал курс микроэкономики и понимает, что в условиях совершенной конкуренции, цену определяет рынок. Миша никак не может влиять на неё, однако он может влиять на то, какое количество газет следует закупить. На втором курсе Миша не учился. Из-за этого он не знает теорию вероятностей и вынужден для решения своих повседневных проблем нанять аналитика. \n",
    "\n",
    "Покупать газету Миша решил по $15$ рублей, а продавать за $30$. Количество потенциальных покупателей - случайная величина с распределением Пуассона. Опытным путём было установлено, что среднее значение этой величины равно $50$. Нераспроданные газеты ничего не стоят. Пусть $n$- количество газет, максимизирующее ожидаемую прибыль Мишы. \n",
    "\n",
    "a) С помощью компьютера найдите оптимальное значение $n$ и ожидаемую прибыль.\n",
    "\n",
    "b) Правильно ли поступил Миша, что бросил учёбу и ушёл в коммерцию? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "449.93796"
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       "449.93796"
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       "[1] 449.938"
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   ],
   "source": [
    "# Ох уж этот Миша!  \n",
    "# Найдём оптимальное количество газет для закупки!\n",
    "\n",
    "n_obs = 10^6  # число наблюдений \n",
    "\n",
    "cost = 15   # издержки на покупку газеты \n",
    "price = 30  # цена, по которой будем продавать газету \n",
    "\n",
    "x = rpois(n_obs, lambda = 50)  # среднее значение совпадает с lambda\n",
    "\n",
    "# посмотрим на прибыль, еслм мы будем продавать 30 газет!\n",
    "# покупатели не могут купить больше 30 газет \n",
    "x[x > 30] = 30  # заменим всё, что больше 30 на 30\n",
    "\n",
    "# найдём все прибыли\n",
    "profit = x*price - 30*cost \n",
    "\n",
    "# найдём среднюю прибыль \n",
    "mean(profit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Отлично! Дело осталось за малым, перебрать все возможноые варианты покупок и выбрать оптимальный \n",
    "\n",
    "profits = rep(0,100) # будем записывать средние прибыли\n",
    "for(s in 1:100){\n",
    "    x = rpois(n_obs, lambda = 50)  # генерируем покупочки \n",
    "    \n",
    "    x[x > s] = s  # нельзя продать лишнее\n",
    "    \n",
    "    profits[s] = mean(x*price - s*cost)  # запоминем среднюю прибыль\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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KlSed1OK2WE/2AdkzfjBF6uMO7hphFT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\nehKgAtaz3yg1CZAACZCA5gT+D4U1io5YQBbYAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Посмотрим на график средней прибыли. Вполне ожидаемо, что это парабола\n",
    "qplot(1:100, profits, geom='line')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "665.61393"
      ],
      "text/latex": [
       "665.61393"
      ],
      "text/markdown": [
       "665.61393"
      ],
      "text/plain": [
       "[1] 665.6139"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "50"
      ],
      "text/latex": [
       "50"
      ],
      "text/markdown": [
       "50"
      ],
      "text/plain": [
       "[1] 50"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Наконец мы видим прибыль Миши и сколько газет ему надо закупать :) \n",
    "max(profits)\n",
    "which.max(profits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# b) На этот пункт у меня для вас ответа нет. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задачка 5\n",
    "\n",
    "Глеб раздобыл кубик и собирается как следует изучить его свойства. Для этого он подбросил его $n$ раз. Величина $X_1$ — число выпадений единицы, а $X_6$ — число выпадений $6$. Глебу интересно какова корреляцие между этими двумя случайными величинами. Что вам на этот счёт подсказывает интуиция? Какой знак будет у этой корреляии: положительным или отрицательным?\n",
    "\n",
    "Оцените с помощью симуляций $Corr(X_1,X_6)$. Пусть $n=10$. Обратите внимание, что $n$ в данном случае это не количество симуляций. Десять подбрасываний это всего лишь одно испытание. После симуляций попытайтесь найти эту корреляцию руками. на бумажке. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "4"
      ],
      "text/latex": [
       "4"
      ],
      "text/markdown": [
       "4"
      ],
      "text/plain": [
       "[1] 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "2"
      ],
      "text/latex": [
       "2"
      ],
      "text/markdown": [
       "2"
      ],
      "text/plain": [
       "[1] 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# подбросим кубик 10 раз и вычислим значения X1 и X6 \n",
    "\n",
    "smpl = sample(size = 10, 1:6, prob = rep(1/6,6), replace = TRUE)\n",
    "\n",
    "sum(smpl == 1) # это X1\n",
    "sum(smpl == 6) # это X6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "-0.20092006602747"
      ],
      "text/latex": [
       "-0.20092006602747"
      ],
      "text/markdown": [
       "-0.20092006602747"
      ],
      "text/plain": [
       "[1] -0.2009201"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^6  # сделаем 10 подбрасываний n раз\n",
    "\n",
    "x1 = rep(0, n_obs)  # сюда будем записывать количество 1 в каждой серии испытаний\n",
    "x6 = rep(0, n_obs)  # сюда будем записывать число 6 в каждой серии испытаний\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    smpl = sample(size = 10, 1:6, prob = rep(1/6,6), replace = TRUE) # первая серия испытаний!\n",
    "    \n",
    "    x1[i] = sum(smpl == 1)\n",
    "    x6[i] = sum(smpl == 6)    \n",
    "}\n",
    "\n",
    "cor(x1, x6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задача 6\n",
    "\n",
    "Случайная величина $X$ распределена равномерно на отрезке $[0;1]$. Женя подкидывает эту случайную величину. Она принимает значение $x$. После подбрасывания Женя изготавливает монетку, которая выпадает «орлом» с вероятностью $x$ и передаёт её Дане. Даня, не зная $x$, подкидывает монетку один раз. Она выпала «орлом». \n",
    "\n",
    "a) Какова вероятность, что она снова выпадет «орлом»?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Вероятность орла на монетке: 0.7324506\n",
      "У Дани выпало: О О"
     ]
    }
   ],
   "source": [
    "# смодулируем одну итерацию всего этого процесса\n",
    "\n",
    "x = runif(1, min = 0, max = 1)        # Женя делает монетку\n",
    "cat('Вероятность орла на монетке:',x)  # Команда cat это более пафосный print\n",
    "\n",
    "# Даня два раза подкидывает монетку\n",
    "y = sample(c('О','Р'), prob = c(x, 1-x), size = 2, replace = TRUE)\n",
    "cat('\\nУ Дани выпало:', y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.568020312581211</li>\n",
       "\t<li>0.138804823858663</li>\n",
       "\t<li>0.768505952088162</li>\n",
       "\t<li>0.0799860621336848</li>\n",
       "\t<li>0.864798867609352</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.568020312581211\n",
       "\\item 0.138804823858663\n",
       "\\item 0.768505952088162\n",
       "\\item 0.0799860621336848\n",
       "\\item 0.864798867609352\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.568020312581211\n",
       "2. 0.138804823858663\n",
       "3. 0.768505952088162\n",
       "4. 0.0799860621336848\n",
       "5. 0.864798867609352\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.56802031 0.13880482 0.76850595 0.07998606 0.86479887"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Отлично! Теперь мы должны сделать как можно больше разных монет и подкинуть их как можно больше раз. \n",
    "# Из-за того, что наш эксперимент происходит последовательно, придётся подкидывать каждую монетку Жени много раз.\n",
    "\n",
    "n_zenia = 100                       # сколько монеток сделал Женя\n",
    "x = runif(n_obs, min = 0, max = 1)  # Женя делает свой ход n_zenia раз\n",
    "x[1:5]                              # первые пять монеток, созданные Женей :) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Знаете, иногда так бывает, что тебе лень что-то делать и ты откладываешь это до лучших времён. \n",
    "# Вот и я отложил. Сейчас, когда я пишу это, до пары остаётся два часа. Можно было бы взять и \n",
    "# написать тут два цикла для генерации вероятностей вместо это текста, но я не хочу их писать. \n",
    "# Они будут большими и страшными. И вообще я бы эту задачку лучше бы убрал из домашки, так как \n",
    "# она для генераций не очень удачная. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Как выглядит ответ, если Дане известно, что монетка при $n$ подбрасываниях $k$ раз выпадала орлом? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ня! Решение пропущено. Или отложено до лучших времён. Не знаю. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "А сможете найти эти вероятности вручную? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задачка 7.1 \n",
    "\n",
    "Пусть $X \\sim Exp(2)$. Аня помнит, что такое распределение называется экспоненциальным и что в такой ситуации функция распределения случайной величины $X$ выглядит как: \n",
    "\n",
    "$$ F(x) = 1 - e^{-2 x}$$\n",
    "\n",
    "Аня хочет понять какое распределение будет у случайной величины $Y$, если \n",
    "\n",
    "$$ Y = 1 - e^{-2 X}$$ \n",
    "\n",
    "Попробуйте ссимулировать такую случайную величину, посмотреть на её гистограмму и дать ответ на вопрос Ани. Подумайте почему ответ получился именно таким."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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J2z2NKkSRNzt8UtW7YEdgi6ZcuWsZOt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\ndCaJAAIIIIAACZhtAAEEEEAAgSQI/B+5QYVlpG+GPgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^6\n",
    "x = rexp(n_obs, rate = 2)\n",
    "y = 1 - exp(-2*x)\n",
    "qplot(y)           # равномерная на отрезке [0; 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задачка 7.2\n",
    "\n",
    "Маша и Виолетта живут в общежитии в одной комнате. Маша постоянно что-то говорит про нейронные сети. Виолетта не очень понимает о чём идёт речь, но хотела бы разобраться, чтобы быть с подругой на одной волне. Для этого она залезла в [мудрую книгу](https://yadi.sk/i/wBswqtL33UDYsD) и стала читать. В одной из первых глав она узнала, что в качестве функции активации в нейронах часто используют сигмоида, которая представляет из себя функцию распределения для логистической случайной величины. Функция выглядит как-то так: \n",
    "\n",
    "$$ F(x) = \\frac{1}{1 + e^{-x}} $$\n",
    "\n",
    "Виолетта пока не поняла что такое нейрон, сигмоида и функция активации, зато она очень хорошо знает что такое распределение случайной величины. Ей жутко интересно как оно выглядит.\n",
    "\n",
    "а) Помогите Виолетте сгенирировать случайную величину $X$, имеющую логистическое распределение. Постройте для неё гистограмму, плотность и функцию распределения прямо как на паре. \n",
    "\n",
    "б) Также Виолетте хотелось бы узнать какое распределение будет у случайной величины $Y = F(X)$. Попробуйте посмотреть на него с помощью симуляций. Как следует подумайте почему ответ получился именно таким. Функция `rlogis` с параметрами `location = 0` и  `scale = 1` вам в помощь! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XZjqVNnEkgjgR07dsjEiRNVtzOSevbZ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\nAAmYRuB/AWkJoVy9ERa5AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a) \n",
    "n_obs = 10^3 # не будем генерировать особо много, а то функция не построится и всё зависнет \n",
    "\n",
    "x = rlogis(n_obs, location=0, scale=1)  #сгенерировали\n",
    "\n",
    "# построим функцию распределения \n",
    "df = data.frame(sample = x)\n",
    "ggplot(df, aes(x = sample)) + stat_ecdf( )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SioqRcB/1pnuPp/TQqqA5ZjaIY2yWAL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\nAnEPgQpumTlUWGgZPOgU9P9aMLqbMPqBMymjdJ/xpKKvviJpio7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fxSNH+/K0E1NkyUH0/Zo03Ln9wf+5h3opU89WPvooNbczctqddGC1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\nlQnQAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# построи гистограмму и плотность \n",
    "ggplot(df, aes(x = sample))+\n",
    "            # Наносим гистограмму \n",
    "            geom_histogram(aes(y = ..density..))+  # опция ..density.. нормирует площадь гистограмы к 1\n",
    "                                                   # попробуйте стереть её и посмотреть что будет \n",
    "             # Наносим плотность распределения\n",
    "            stat_function(fun = dlogis, args = c(0,1), color = \"darkred\", size=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cdbHz0/zjAJ2JHgEQEEEEgsgUROwAlz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\nbKV7v126d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XX3+9dO3aVTp27GgSsV5g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\nwlQAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# b) сгенерируем выборку в нормальном объёме \n",
    "n_obs = 10^6\n",
    "x = rlogis(n_obs, location=0, scale=1)  #сгенерировали\n",
    "\n",
    "y = 1/(1 + exp(-x))\n",
    "qplot(y)           # равномерная на отрезке [0; 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Воу, воу, воу, теория вероятностей, палехче! В обеих задачах получился одинаковый ответ. Видимо, в случайной величине $Y = F(X)$, где $F(x)$ - функция распределения случайной величины $X$, есть какая-то магия. Подумайте о том какая и постарайтесь доказать наличие этой магии на бумаге. На семинаре мы попробуем сделать это совместно. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задачка 9 \n",
    "\n",
    "Было бы нечестно, если после задач $7.1$ и $7.2$ следовала бы задачка с номером $8$. Поэтому тут задачка с номером $9$! \n",
    "\n",
    "Есть две монеты, у которых вероятности выпадения орла при однократном подбрасывании равны $0.6$ и $0.4$. Камила подбрасывает первую монетку до появления орла. Вика делает то же самое со второй монеткой. Найдите с помощью симуляций вероятность того, что \n",
    "\n",
    "a) Вика сделает больше подбрасываний, чем Камила;\n",
    "\n",
    "b) Камила сделает больше подбрасываний, чем Вика;\n",
    "\n",
    "c) Камила и Вика сделают одинаковое число подбрасываний.\n",
    "\n",
    "d) Верно ли, что в сумме эти три вероятности дают единицу? Логично ли это? \n",
    "\n",
    "e) Найдите математическое ожидание суммарного количества бросков. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>0</li>\n",
       "\t<li>1</li>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 0\n",
       "\\item 1\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 3\n",
       "3. 1\n",
       "4. 2\n",
       "5. 0\n",
       "6. 1\n",
       "7. 0\n",
       "8. 0\n",
       "9. 0\n",
       "10. 0\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 0 3 1 2 0 1 0 0 0 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^6\n",
    "p1 = 0.6\n",
    "p2 = 0.4 \n",
    "\n",
    "# симулируем подбрасывания Вики и Камилы\n",
    "x_kamila = rgeom(n_obs, prob = p1)\n",
    "x_vika = rgeom(n_obs, prob = p2)\n",
    "\n",
    "x_kamila[1:10]  # в векторе стоит число подбрасываний до первого орла"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.473891"
      ],
      "text/latex": [
       "0.473891"
      ],
      "text/markdown": [
       "0.473891"
      ],
      "text/plain": [
       "[1] 0.473891"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a)  # логично, Вике больше повезло с монткой!\n",
    "sum(x_vika > x_kamila)/n_obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.211154"
      ],
      "text/latex": [
       "0.211154"
      ],
      "text/markdown": [
       "0.211154"
      ],
      "text/plain": [
       "[1] 0.211154"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# b) \n",
    "sum(x_vika < x_kamila)/n_obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.314955"
      ],
      "text/latex": [
       "0.314955"
      ],
      "text/markdown": [
       "0.314955"
      ],
      "text/plain": [
       "[1] 0.314955"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# c) \n",
    "sum(x_vika == x_kamila)/n_obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1"
      ],
      "text/latex": [
       "1"
      ],
      "text/markdown": [
       "1"
      ],
      "text/plain": [
       "[1] 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# d) \n",
    "# да, эти вероятности дадут в сумме единицу, потому что других исходов не бывает\n",
    "sum(x_vika > x_kamila)/n_obs + sum(x_vika < x_kamila)/n_obs + sum(x_vika == x_kamila)/n_obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.16823"
      ],
      "text/latex": [
       "2.16823"
      ],
      "text/markdown": [
       "2.16823"
      ],
      "text/plain": [
       "[1] 2.16823"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# e) \n",
    "mean(x_vika + x_kamila)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Продемонстрируйте с помощью симуляций, что у геометрического распределения нет памяти. Определение [отсутствия памяти ищи тут](https://ru.wikipedia.org/wiki/Геометрическое_распределение). Что это означает для Вики и Камилы? \n",
    "\n",
    "Читаем определение! У распределения нет памяти, если количество прошлых неудач не влияет на количество будущих неудач\n",
    "\n",
    "$$ P( Y >  m + n \\mid Y \\ge m) = P(Y > n).$$ \n",
    "\n",
    "Ровно это и закодим."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.4094854"
      ],
      "text/latex": [
       "0.4094854"
      ],
      "text/markdown": [
       "0.4094854"
      ],
      "text/plain": [
       "[1] 0.4094854"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs <- 10^7\n",
    "p <- 0.2 \n",
    "\n",
    "y <- rgeom(n_obs, prob = p)\n",
    "\n",
    "sum(y > 3)/n_obs  # Правая часть равенства "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.409932151066872"
      ],
      "text/latex": [
       "0.409932151066872"
      ],
      "text/markdown": [
       "0.409932151066872"
      ],
      "text/plain": [
       "[1] 0.4099322"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Левая часть равенства \n",
    "y = y[y >= 2] \n",
    "sum(y > 2 + 3)/length(y)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Эту задачку тоже можно решить руками на бумаге. Слабо? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задачка 10\n",
    "\n",
    "Света очень долго сидела и думала. В конечном счёте у неё возникло очень много разнообразных вопросов. Помогите Свете ответить на них. \n",
    "\n",
    "a) Пусть $X \\sim N(5,9)$, а $Y \\sim N(3, 16)$. Верно ли, что сумма нормальных случайных величин будет нормальной случайной величиной? Какими будут математическое ожидние и дисперсия у итоговой случайной величины.  Проверьте это с помощью симуляций.\n",
    "\n",
    "___ВНИМАНИЕ:___ код с симуляциями ни в коем случае не является доказательством верных фактов, их строгие доказательства можно найти в лекциях. Но при этом он является опровержением неверных фактов. Помните о том, что в математике да это всегда да, а нет это хотя бы один раз нет. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "7.97670523186983"
      ],
      "text/latex": [
       "7.97670523186983"
      ],
      "text/markdown": [
       "7.97670523186983"
      ],
      "text/plain": [
       "[1] 7.976705"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "25.509984878305"
      ],
      "text/latex": [
       "25.509984878305"
      ],
      "text/markdown": [
       "25.509984878305"
      ],
      "text/plain": [
       "[1] 25.50998"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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ouLZeHChUF5unXrJvXq1TPjNc/8+fNN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\nCCAQSYH/ByWyhDgGVAoqAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^4\n",
    "x <- rnorm(n_obs, mean=5, sd=3)  # обратите внимание, что мы указываем sd а не дисперсию!\n",
    "y <- rnorm(n_obs, mean=3, sd=4)\n",
    "\n",
    "mean(x+y)     # 8 = 5 + 3     всё как в лекциях!\n",
    "var(x+y)      # 25 = 9 + 16   снова всё как в лекциях!\n",
    "qplot(x + y)  # посмотрим на гистограмку :3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Пусть $X \\sim N(\\mu, \\sigma^2)$. Верно ли, что $\\frac{X-\\mu}{\\sigma} \\sim N(0,1)$? Проверьте это с помощью симуляций. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.00967422247549304"
      ],
      "text/latex": [
       "0.00967422247549304"
      ],
      "text/markdown": [
       "0.00967422247549304"
      ],
      "text/plain": [
       "[1] 0.009674222"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1.02516711271094"
      ],
      "text/latex": [
       "1.02516711271094"
      ],
      "text/markdown": [
       "1.02516711271094"
      ],
      "text/plain": [
       "[1] 1.025167"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IBAuIDjVtB6G9B3v/vdsOBrX6S+qlAfwqEvQ6BDAAEEEEAAgegCjo+AtXVXXc+5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\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# конечно верно! такая процедура называется стандартизацией случайной величины \n",
    "# хорошо бы попробовать код для разных примеров нормальных случайных величин\n",
    "\n",
    "x = rnorm(n_obs, mean=5, sd=3)\n",
    "y = (x - 5)/3\n",
    "mean(y)\n",
    "var(y)\n",
    "qplot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "с) Пусть $X \\sim U[0;1]$ и $Y \\sim U[0;1]$. Верно ли, что $X + Y$ также будет иметь равномерное распределение? Проверьте это с помощью симуляций? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XRt1oSEBN+d6xQrNTXVFbO4D8CqrgeN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\nAEE+jd8AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# конечно неверно, это чушь! сумма равномерных величин иметт распределение треугольника\n",
    "\n",
    "x <- runif(n_obs, min = 0, max = 1)\n",
    "y <- runif(n_obs, min = 0, max = 1)\n",
    "qplot(x+y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d) Пусть $X \\sim U[0;1]$. Какое распределение будет у $Y = 5 + 3\\cdot X$? Узнайте это с помощью симуляций. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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S9VqqyslKqqKpk8ebLoTGk9rM2CAAII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\nv49pIQIIIICADwX+B0cm1YurM/ZiAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# она будет равномерной на отрезке от 5 до 8 :) \n",
    "# мы сдвинули распределение вправо на 5 и растянули в три раза\n",
    "\n",
    "x <- runif(n_obs, min = 0, max = 1)\n",
    "y = 5 + 3*x\n",
    "qplot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Когда сумма случайных величин из одного семейства даёт случайную величину из этого же семейства, то такое распределение называется устойчивым относительно суммирования. Получилось ли, что нормальное и равномерное распределения устойчивы относительно суммирования?  Как думает распределение Пуассона, экспоненциальное и Хи-квадрат устойчивы относительно суммирования? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Найдите в лекциях по теории вероятностей весь материал, который касается свойств нормального распределния и повторите его. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}