{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "\n", "#
R для тервера и матстата.

2. Варка распределений, ЗБЧ, метод Монте-Карло.
\n", "\n", "Данный ноутбук является конспектом 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", "В этой терадке мы поговорим о варке распределений, методе монтекрало и законе больших чисел. Будет мног симуляций. Добро пожаловать. Уже традиционно, начнём с подгрузки пакетов, часть из которых при работе в RStusio можно проигнорировать. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "library(\"ggplot2\") # Пакет для красивых графиков \n", "library(\"grid\") # Пакет для субплотов\n", "\n", "\n", "# Эти пакеты для Rstudio не очень то и нужны \n", "# Отрегулируем размер картинок, которые будут выдаваться в нашей тетрадке\n", "library('repr')\n", "options(repr.plot.width=4, repr.plot.height=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Варка распределений\n", "\n", "Помните задачку $7.1$ и задачку $7.2$ из домашнего задания? Пришло время понять что за тайна скрывается за этими двумя задачами! Для начала, давайте разберёмся как они решаются. \n", "\n", "### 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": 4, "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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3nqLWiWL+jLV4sWLayioqLBbZTlJht9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\nEM1IJRBAAAEEkibwf8AvxM+SLsDKAAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x <- rexp(10^6, rate = 2)\n", "qplot(x)" ] }, { "cell_type": "code", "execution_count": 5, "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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Q8ePNhrschHAAEEsl5AG2exqWnTpuZu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\nQNo5a8yYM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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y <- 1 - exp(-2*x)\n", "qplot(y)" ] }, { "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": 6, "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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QABOBMllkEAAQQQQMBnAQKwz6AUhwAC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\nQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x <- rlogis(10^6, location = 0, scale = 1)\n", "qplot(x)" ] }, { "cell_type": "code", "execution_count": 7, "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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VwWcPF9rp2S9SmBfiVwAtag8+bNM72g9XxwbI9n3evV4Z///Od+06UeAQQQQACB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\nAAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y <- 1/(1 + exp(-x))\n", "qplot(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Дважды у нас получилось равномерное распределение. Знакомьтесь с ещё одной интересной теоремой, которая наравне с ЗБЧ и ЦПТ позволяет нам делать многие интересные вещи. \n", "\n", "#### Теорема:\n", "\n", "Пусть функция распределения $F_X(x)$ непрерывна. Тогда случайная величина $Y = F(X)$ имеет равномерное распределение на отрезке $[0; 1]$.\n", "\n", "___Доказательство:___\n", "\n", "Найдём функцию распределения случайной величины $Y$. Заметим, что всегда $0 \\le Y \\le 1$ в силу области определения функции распределения $F(x)$. Предположим сначала, что функция $F$ всюду возрастает, тогда она обратима и поэтому: \n", "\n", "$$\n", "F_Y(y) = P(F(X) < y) = P(X < F^{-1}(y)) = F(F^{-1}(y)) = y, \\text{ если } x \\in (0,1).\n", "$$\n", "\n", "При этом мы знаем, что функция распределения $F(y) = y$ соответствует равномерному на отрезке $[0;1]$ распределению. \n", "\n", "Если функция $F$ не является всюду возрастающей, то у неё есть участки постоянства.В этом случае просто обозначим через $F^{-1}(y)$ самую левую точку из замкнутого множества $\\{t \\mid F(t) = x\\}$. При таком понимании обратной функции все равенства, перичесленные выше, остаются справедливы. \n", "\n", "___ч.т.д.___ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Это многое объясняет. Давайте посмотрим на нашу теорему немного с другой стороны. \n", "\n", "___Cледствие:___\n", "\n", "Пусть $Y \\sim U[0;1]$, а $F$ — произвольная функция распредения. Тогда случайная величина $X = F^{-1}(Y)$ (квантильное преобразование над $Y$) имеет функцию распределения $F$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "На лекции мы с вами обсудили, что генерация случайностей это довольно сложное занятие. Равномерная случайная величина одна из самых приятных в плане генерации. Обычно алгоритмы генерации создают именно для неё, так как с более сложными распределениями возникают проблемы. Квантильное преобразование позволяет нам расширить навыки компьютера и переработать равномерную случайную величину в необходимое нам распределение. Снова математика позволила нам быть клёвыми. Приятно. \n", "\n", "Как же мы можем сварить из равномерной случайной величины, $U[0; 1]$ экспоненциальную величину, $Exp(\\alpha)$? Легко! \n", "\n", "$$\n", "F_X(x) = 1 - e^{-\\alpha x}\n", "$$\n", "\n", "$$\n", "F_X^{-1}(y) = -\\frac{1}{\\alpha} \\ln(1-y). \n", "$$\n", "\n", "Все выкладки проведены, давайте варить!" ] }, { "cell_type": "code", "execution_count": 8, "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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8a3cussn4/7iD6TH3zwQa19eKK6r+sgTQc7vu0jOuDR90mqlHEAVi9oBeF169Yl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\nWAgQgGNRjWwEAggggIBvAv8PXQmyDx970h8AAAAASUVORK5CYII=", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y <- runif(10^6, min = 0, max = 1)\n", "x <- -0.5*log(1-y)\n", "qplot(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Вот и все дела. Аналогично можно попробовать получить какую-нибудь случайно величину с заранее известной функцией распределения. Давайте попробуем получить случайную величину со следующей функцией распределения: \n", "\n", "$$\n", "F(x) = \\begin{cases} 0, x < 0 \\\\ x^7, x \\in [0,1] \\\\ 1, x > 1 \\end{cases}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Согласитесь, найти обратную функцию здесь довольно просто... " ] }, { "cell_type": "code", "execution_count": 9, "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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5jbUlegOoS9LbWeYW7Lqsto1c/Wbzbd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\n6KFp06bmE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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y = runif(1000, min = 0, max = 1)\n", "x = y^(1/7)\n", "qplot(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ясное дело, что работать такая схема будет не всегда. Например, её никогда не используют для нормального распределения. Проблема в том, что подсчет обратной функции распределения для него аналитически невозможен, так как интеграл \n", "\n", "\n", "$$ \n", "F(x) = \\int_{-\\infty}^{x} \\frac{1}{\\sigma \\sqrt{2 \\pi}} \\cdot e^{-\\frac{(t-\\mu)^2}{2 \\sigma^2}} dt\n", "$$\n", "\n", "не берётся. Немного подробнее про разные генераторы случайных чисел можно [почитать на хабре.](https://habrahabr.ru/post/263993/)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Закон больших чисел\n", "\n", " \n", "\n", "\n", "### 2.1 Игра в кости\n", "\n", "В презентации мы увидели забавную [иллюстрацию ЗБЧ, взятую с википедии.](https://ru.wikipedia.org/wiki/Закон_больших_чисел) Давайте попробуем воспроизвести её в R! \n", "\n", "Итак, у нас есть игральная кость. Нам хочется узнать какое среднее значение на ней будет выпадать при увеличении количества бросков. Напишем цикл, который будет симулировать подбрасывание кости и записывать среднее значение в заранее заготовленный вектор." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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x3kGUN9ghF1gOlVpuCbGd5xznenW62b03lgRmHPPfeMnR/CJN90UE444YRmUQy7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\nxysV2rybdn6nnVeFpTeINfLfyaODLA+VZXgkq11Dh1aGtXJ2J7c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bx7Tx4GZlKogRMKM6TXmmbvCnsLhxlSeOGk3AI01nup6IG+KhF63R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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_obs = 1000\n", "kubik = rep(0, n_obs)\n", "\n", "for(n in 1:n_obs){ # n - количество подбрасываний кубика\n", " \n", " # Сделали выборку \n", " smpl = sample(1:6, size = n, replace = TRUE)\n", " \n", " # Подсчитали среднее значение и запомнили его \n", " kubik[n] = mean(smpl) \n", "}\n", "\n", "qplot(1:1000, kubik, geom='line', xlab='number of observations', ylab='result')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Мы видим, что cреднее значение, выпадающее на кости, сходится по вероятности к истиному математическому ожиданию, о чём нам и говорит ЗБЧ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2 Страховка\n", "\n", "Закон больших чисел — это теорема, которая позволяет людям зарабатывать деньги! В 1600-х годах люди научились состовлять актуарные таблицы. Это такие таблицы, где указана ожидаемая продолжительность жизни для данного возраста и пола. Люди начали собирать данные о смертности и оценивать вероятность дожития человека до определённого возраста. На этом строились тарифы на страхование. \n", "\n", "Появление подобных таблиц обязано зарождению в течение 1600-х годов теории вероятности, которая впервые объяснила людям как случайные вещи при достаточно больших масштабах сглаживаются и становятся очень даже предсказуемыми. Надо признать, что у страхования было довольно трудное детство — как раз потому, что люди плоховато понимали концепцию вероятности. В голове довольно трудно удержать её. Многие люди и по сей день ошибочно думают, что могут влиять на случайность каким-то образом. Например, некоторые думают, что чаще других выбрасывают на кубике шестёрки. Более того, люди довольно плохо понимают условные вероятности. \n", "\n", "Несмотря на всё это недопонимание, страховые компании в наше время на диверсификации рисков делают довольно неплохой бизнес. Текущее упражнение призвано показать как примерно это происходит. Давайте представим, что мы с вами решили запилить свой собственный бизнес, связанный со страховками.\n", "\n", "Конечно же бизнес мы будем делать в России. Для того, чтобы как следует сделать его, мы нашли [актуарные таблицы для России 2009 года выпуска.](https://yadi.sk/i/-k-9kB263Uv8uH)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
XМужчины.и.женщины.городМужчины.городЖенщины.городМужчины.и.женщины.селоМужчины.селоЖенщины.село
0 лет 0.9925250.9916580.9934420.9903210.9892090.991496
1 год 0.9993070.9992210.9993970.9988120.9987090.998921
2 года 0.9995580.9995170.9996010.9993580.9992980.999420
3 года 0.9996680.9996090.9997300.9994410.9992880.999601
4 года 0.9997000.9996710.9997310.9995240.9994450.999607
5 лет 0.9996950.9996360.9997570.9995150.9994440.999589
\n" ], "text/latex": [ "\\begin{tabular}{r|lllllll}\n", " X & Мужчины.и.женщины.город & Мужчины.город & Женщины.город & Мужчины.и.женщины.село & Мужчины.село & Женщины.село\\\\\n", "\\hline\n", "\t 0 лет & 0.992525 & 0.991658 & 0.993442 & 0.990321 & 0.989209 & 0.991496\\\\\n", "\t 1 год & 0.999307 & 0.999221 & 0.999397 & 0.998812 & 0.998709 & 0.998921\\\\\n", "\t 2 года & 0.999558 & 0.999517 & 0.999601 & 0.999358 & 0.999298 & 0.999420\\\\\n", "\t 3 года & 0.999668 & 0.999609 & 0.999730 & 0.999441 & 0.999288 & 0.999601\\\\\n", "\t 4 года & 0.999700 & 0.999671 & 0.999731 & 0.999524 & 0.999445 & 0.999607\\\\\n", "\t 5 лет & 0.999695 & 0.999636 & 0.999757 & 0.999515 & 0.999444 & 0.999589\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "X | Мужчины.и.женщины.город | Мужчины.город | Женщины.город | Мужчины.и.женщины.село | Мужчины.село | Женщины.село | \n", "|---|---|---|---|---|---|\n", "| 0 лет | 0.992525 | 0.991658 | 0.993442 | 0.990321 | 0.989209 | 0.991496 | \n", "| 1 год | 0.999307 | 0.999221 | 0.999397 | 0.998812 | 0.998709 | 0.998921 | \n", "| 2 года | 0.999558 | 0.999517 | 0.999601 | 0.999358 | 0.999298 | 0.999420 | \n", "| 3 года | 0.999668 | 0.999609 | 0.999730 | 0.999441 | 0.999288 | 0.999601 | \n", "| 4 года | 0.999700 | 0.999671 | 0.999731 | 0.999524 | 0.999445 | 0.999607 | \n", "| 5 лет | 0.999695 | 0.999636 | 0.999757 | 0.999515 | 0.999444 | 0.999589 | \n", "\n", "\n" ], "text/plain": [ " X Мужчины.и.женщины.город Мужчины.город Женщины.город\n", "1 0 лет 0.992525 0.991658 0.993442 \n", "2 1 год 0.999307 0.999221 0.999397 \n", "3 2 года 0.999558 0.999517 0.999601 \n", "4 3 года 0.999668 0.999609 0.999730 \n", "5 4 года 0.999700 0.999671 0.999731 \n", "6 5 лет 0.999695 0.999636 0.999757 \n", " Мужчины.и.женщины.село Мужчины.село Женщины.село\n", "1 0.990321 0.989209 0.991496 \n", "2 0.998812 0.998709 0.998921 \n", "3 0.999358 0.999298 0.999420 \n", "4 0.999441 0.999288 0.999601 \n", "5 0.999524 0.999445 0.999607 \n", "6 0.999515 0.999444 0.999589 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df = read.csv('data/aktuar2009.csv', sep=';', dec=',')\n", "head(df)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Посмотрим на то как в России выживается женщинам и мужчинам." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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wVXjiZXUsNatQ29297s6ALbzy/lcIaX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", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df['age'] = 0:100\n", "df['man_prob'] = cumprod(df[,3]) # вероятность дожить до какого-то возраста\n", "df['woman_prob'] = cumprod(df[,4])\n", "\n", "ggplot(df, aes(age))+\n", " geom_line(aes(y=man_prob, colour = \"man\"))+\n", " geom_line(aes(y=woman_prob, colour = \"woman\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Красота спасёт мир! Давайте застрахуем мир от гибели. Предположим, что наша страховая компания собирается страховать жизни красивых девушек. Страховки продаются на год. Только девушкам возраста от 20 до 60. Для каждого возраста надо установить некоторую величину страхового взноса. Давайте попробуем найти минимально допустимую величину для каждого возраста. Для этого решим небольшую подготовительную задачку. \n", "\n", "__Подготовительная задачка:__ \n", "\n", "Пусть для 25-летней девушки вероятность прожить ещё год составляет $0.9$. Страховка на год стоит $1000$ рублей при взносе в $110$ рублей. Какой будет средняя прибыль страховой компании с одной страховки? \n", "\n", "Пусть случайная величина $X_i$ - прибыль с одной страховки. Если девушка прожила ещё год, то мы получаем в пользование компании $110$ рублей. Если с девушкой что-то произошло, мы должны выплатить её семье $1000$ рублей. Прибыль компании составит $-890$ рублей. \n", "\n", "| $X_i$ | $110$ | $-890$ | \n", "|---|---|---|\n", "| | 0.9 | 0.1 |\n", "\n", "Средняя прибыль компании составит $\\frac{1}{n} \\sum X_i$. По закону больших чисел\n", "\n", "$$\n", "\\frac{1}{n} \\sum X_i \\to E(X_1) = 0.9 \\cdot 110 - 0.1 \\cdot 890 = 10\n", "$$\n", "\n", "Значит средняя прибыль компании с одной страховки составит $10$ рублей. Поздравляю! Мы не работаем себе в убыток. Хорошо. Тепер, когда мы решили подготовительную задачку, мы можем начать страховать красоток. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Давайте попробуем подобрать под такую сумму выплат страховой взнос. Будем обозначать взнос как $z$, а сумму выплат как $N$. Ожидаемая прибыль составит \n", "\n", "$$\n", "E(X) = p \\cdot z + (1 - p) \\cdot (z - N).\n", "$$\n", "\n", "Приравняв это добро к нулю и решая уравнение, получаем минимальный необходимый для нормального функционирования фирмы взнос\n", "\n", "$$\n", "z = (1-p) \\cdot N.\n", "$$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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a8hODm+YAwkQAGOgUJkFkiABEggmgQwZwCan/PkySM9e/aMpilGXZsCbFRx0VgS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", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 10^6\n", "z = c( )\n", "\n", "for(p in probs){\n", " z = append(z,(1-p)*N )\n", " }\n", "\n", "qplot(1:length(z),z, geom='line')" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "3298.00000000002" ], "text/latex": [ "3298.00000000002" ], "text/markdown": [ "3298.00000000002" ], "text/plain": [ "[1] 3298" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "z[25] # страховой взнос 25-летней дамы \n", "# ясное дело, что недостаточно просто посмотреть на безубыточный взнос и поставить его \n", "# нужно ещё и на спрос смотреть, но это уже сложно и мы это делать не будем" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Вот такие страховые взносы. Давайте ради интереса посмотрим насколько сильно нам придётся обделить мужчин. " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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/s7adKkSczLVj4DKNHLL79czjvvPJk5c6a2QlFmKM177rlHzj//fPn666/loYce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\nL1sp8IaZNXT8VJUG4puwuiqsrlKkW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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df['age'] = 0:100\n", "df['w_ensh'] = (1 - df$'Женщины.город')*N\n", "df['m_ensh'] = (1 - df$'Мужчины.город')*N\n", "\n", "ggplot(df, aes(age))+\n", " geom_line(aes(y=m_ensh, colour = \"man\"))+\n", " geom_line(aes(y=w_ensh, colour = \"woman\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Мужчинам страховка обходится подороже. Мрут как мухи. Вот такая вот история по спасению красоты. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.3 Скорость работы кода \n", "\n", "В R можно измерить скорость работы кода. Для этого есть целый пакет. Он называется `microbenchmark`. В этом пакете есть только одна команда. Как это не удивительно, она также называется `microbenchmark`. У вас на компьютерах, скорее всего, нет этого пакета. Его нужно один разок установить командой `install.packages(\"microbenchmark\")`. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "library(\"microbenchmark\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Эта команда прогоняет код, который находится внутри неё $100$ раз и выдаёт кучу разной информации об этих прогонах. Зачем $100$ раз? Дело в том, что время работы кода является случайной величиной. Компьютер это живой организм, внутри которого происходит огромное количество разных процессов. Возможно, что при конкретном прогоне кода, у вас на заднем фоне заиграл шикарный бит из [альбома, записанного для фильма Чёрная Пантера,](https://music.yandex.ru/album/5040468) и из-за этого программа работала немного дольше, чем обычно. Нам бы хотелось узнать медианное время работы кода. \n", "\n", "Например, посмотрим как долго работает операция \"Квадратный корень\". " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Unit: microseconds\n", " expr min lq mean median uq max neval\n", " sqrt(x) 1.045 1.0850 11.65188 1.112 1.161 1049.925 100\n", " x^0.5 6.000 6.0435 6.15289 6.071 6.130 12.112 100\n" ] } ], "source": [ "x = sample(100)\n", "\n", "t <- microbenchmark(\n", " sqrt(x),\n", " x ^ 0.5\n", ")\n", "\n", "print(t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Забавно но встроенная команда `sqrt` извлекает квадратный корень намного быстрее, чем команда `x^0.5`. Как думаете с чем это связано? \n", "\n", "В протоколе кроме среднего выводится ещё и медиана. Медиана - это когда половина результатов эксперимента больше, а половина меньше этой цифры. Она довольно часто используется в статистике - зарплату по регионам корректнее сравнивать не среднюю, а медианную, потому что очень маленькие или очень большие зарплаты искажают реальную картину. А на медиану они не влияют. Говорят, что медиана устойчива к выбросам. \n", "\n", "Давайте попробуем посмотреть на распределения времени работы кода. В этом распределении чётко можно увидеть выбросы. " ] }, { "cell_type": "code", "execution_count": 19, "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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Dh99NFHm0WLFrkWsfZpVisZgQAEIAABCEAgmkDRClgnER122GGupZvrZK9evcyP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\nlU3HHmrjFq0Jzyc+b+t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IUABCAAAQjE\nQgAFHAtWHIUABCAAAQg0TeD/AIGh7sY6F7e1AAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "qplot(t[t$expr == 'sqrt(x)',]$time)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Также можно построить на одном графике сразу обе плотности распределения. Они будут красивого кремового цвета." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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+iGVqxSuOGGG9wCHBdddJF98MEHsW61Vy0kSAQCEIAABGoNAe1b8Omnn5bxZ+bM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\nHs8hAAEIQMAjgf8DQy/55gApm1MAAAAASUVORK5CYII=", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggplot(t, aes(x=time, fill=expr)) + geom_density(alpha=0.25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Для этого пакета можно построить картинки с названием виолончель! На них можно увидеть где примерно концентрируются значения случайной величины." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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vupVrzs5xcB3q/Z/EvQ54P7jCi3hm60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\nhbmNN9646GiOOeaYfJsGP9hR9Has6K8APeBGfV1h5SwJHH744Wb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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "autoplot(t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Про визуализации мы позже поговорим отдельно. Если вы не понимаете как делать их, не расстраивайтесь! Это почти всегда гуглинг и копи-паста уже готового кода с минимальными правками. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Монте-Карло \n", "\n", "Мо́нте-Ка́рло (монегасский Monte-Carlu, фр. Monte-Carlo) — административная территория княжества Монако, крупнейший район страны, расположенный на территории одноименной коммуны в Монако. Город известен своими казино, пляжами и пользуется популярностью у представителей высшего общества. В Монте-Карло начинается и завершается ежегодное ралли «Монте-Карло».\n", "\n", "![Фото Монте-Карло](http://seductrice.ru/public-pics/2016/11/monte-carlo_vecher.jpg)\n", "\n", "Так говорит Википедия. Но мы будем говорить про метод работы со случайными числами, которые раньше генерировали рулеткой, коих много в Монте-Карло.\n", "\n", "## Метод Монте-Карло для поиска площади фигуры \n", "\n", "Как найти площадь под графиком $\\cos(x)$ от $0$ до $\\pi/2$. Можно вспомнить, что это $\\sin(\\pi/2) - \\sin(0) = 1$. Но допустим, все лекции и семинары по матану вы прогуляли. Тогда можно поступить так: Впишем график в прямоугольник $(0,0) : (\\pi/2,1)$, он точно весь туда помещается. И теперь сгенерируем парочку точек в этом прямоугольнике. " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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7vCQ0BLao+H+f55pfGjTcx3X6RgFgvopWW0prKesqqSmnHHOpZYtLpcGKkp6u4v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CBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBB7LAv8FNfY6Pczy0/wA\nAAAASUVORK5CYII=", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width=6, repr.plot.height=5)\n", "\n", "p <- seq(0,pi/2, by=0.005)\n", "plot(p, cos(p), type=\"l\") # график\n", "x <- runif(10, min=0, max=pi/2)\n", "y <- runif(10, min=0, max=1)\n", "points(x, y, col=ifelse(y > cos(x),\"red\",\"darkgreen\"), cex=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Площадь всего прямоугольника будет равна $1 \\cdot \\pi/2 = \\pi/2$. Заметим, что только часть точке попала под кривую. Утверждается, что доля точек, лежащих под кривой, умноженная на площадь прямоугольника стремится к истинной площади под кривой. Продемонстрирую свою мысль:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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fZ68r+U1GP9Iz7UV2qX+lZ9JpxS/uq5tpHkQCJsBr8ojHa6LKXq6ko+eM6Px96L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4qkvESeLG0PQifvll/DcU/Efq57g9m6ie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\nz6rmOV9IzPmwy9vrflXylAg0qaWm4LGCJKRnaHmkXyyoic92E5GzaYvTYzR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qvPyCUtfBLoMx6ef5h13K+bwa1kE2C8Qd+GVq7slkfiqV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\nJXw93CdjMsin69Av4s9ecHzCwwkB6tOPuGTay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82j6tUKzpcunJnOA5iB0KJzN2iGuEAB80WU0zSgGXlSD/EJ33oRGNTxZtfbcOIOrNLH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LuvaJE+nOxCtwzWKaeY7ZvSuC8RYMvBnUegBp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\nDnCzieExdFGOyTTIDGhjkec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uqB+w5x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\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Upfj7kVJ1mVdMyDdO+D+9fEUcRnTdzS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gCL9DRXfHwkXvL5EvZXFQckNeks5Nv1rc3pY3TFHyMe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\nVuNCwviOUWxcVW5Dp3kLoi3G+zya0MYo779A0Ev4bcqTNCN98zubmx8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8yjzZtmqxZBs04RF+uY8BucEfLL929+D9LRqsaUCOjrSEgI6O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\nqNnArMCs9qD+vNZNpn2UYcSfxi9CTMqpzdUoHhKfnCy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/wnI/Ml/ZqsStAr/Af0pR7rmkV433CHBvUn4Pe+2D+xrCPuZ5Ang1gZ/XeOX9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\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Dppelx7IePl1lreSKdUy+L3PLpHWdu+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\nzQgeptVg0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+ofW7Is+rmYRfpb6vq58D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1NvNabP5ODVA5i82PpQYYcSdSlhVhOQ5j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\nHPLImGb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jv0ptxnkM6ldND7SeCL+L3D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\nGVi6Y8cOzXQurcu089hlvitpKdgATp0nrXRnkFkeU2E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YgR1LykmbbTmNwCQIu2K0K0l49qtxpxDgBk/tO+cCMs86LsJ34V37yy+II0N1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\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/jzHv4zszbkyRhSK83N7umu6BGYaFwG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r3uHAt/k5DbVnPdGdMqrZaAa2vMzciwmOjHCM4Ub4v9WQZqUl65REDRGM5x2x8+IH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\nol9A34jWSRvlZ6J1UPwU9B3ou9Gr5zxePF4BpQ321am0wsC5+1YmYAImYAI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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(p, cos(p), type=\"l\")\n", "x <- runif(10^4, min=0, max=pi/2)\n", "y <- runif(10^4, min=0, max=1)\n", "points(x, y, col=ifelse(y > cos(x),\"red\",\"darkgreen\"))" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.990544163676862" ], "text/latex": [ "0.990544163676862" ], "text/markdown": [ "0.990544163676862" ], "text/plain": [ "[1] 0.9905442" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sum(y\n", "\t
  • 0
  • \n", "\t
  • 3
  • \n", "\t
  • 4
  • \n", "\t
  • 2
  • \n", "\t
  • 7
  • \n", "\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 0\n", "\\item 3\n", "\\item 4\n", "\\item 2\n", "\\item 7\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 0\n", "2. 3\n", "3. 4\n", "4. 2\n", "5. 7\n", "\n", "\n" ], "text/plain": [ "[1] 0 3 4 2 7" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# генерируем номер телефона\n", "sample(size = 5, 0:9, replace = FALSE)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
      \n", "\t
    1. 0
    2. \n", "\t
    3. 1
    4. \n", "\t
    5. 0
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    7. 0
    8. \n", "\t
    9. 1
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    \n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 0\n", "\\item 1\n", "\\item 0\n", "\\item 0\n", "\\item 1\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 0\n", "2. 1\n", "3. 0\n", "4. 0\n", "5. 1\n", "\n", "\n" ], "text/plain": [ "[1] 0 1 0 0 1" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# проверяем все цифры на чётность \n", "sample(size = 5, 0:9, replace = FALSE) %% 2" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "3" ], "text/latex": [ "3" ], "text/markdown": [ "3" ], "text/plain": [ "[1] 3" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# смотрим сколько в сумме нечётных цифр\n", "sum(sample(size = 5, 0:9, replace = FALSE) %% 2)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.099445" ], "text/latex": [ "0.099445" ], "text/markdown": [ "0.099445" ], "text/plain": [ "[1] 0.099445" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# и всё это в цикле!\n", "n_obs = 10^6\n", "\n", "m = 0\n", "for( i in 1:n_obs){\n", " # если 4 нечётные, значит одна чётная\n", " if(sum(sample(size = 5, 0:9, replace = FALSE) %% 2) == 4){\n", " m = m + 1\n", " }\n", "}\n", "\n", "m/n_obs" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.0992063492063492" ], "text/latex": [ "0.0992063492063492" ], "text/markdown": [ "0.0992063492063492" ], "text/plain": [ "[1] 0.09920635" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Настоящая вероятность: \n", "(5*5*5*4*3*2)/(10*9*8*7*6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.2 Море и спортсмены \n", "\n", "Для $20$ участников соревнований, среди которых $8$ российских, в гостинице забронировано $20$ номеров. Из них $12$ с видом на море. Участники соревнований наугад получают ключи от номернов. Найдите вероятность того, что номера с видом на море достанутся всем российским спортсменам. " ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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    \n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'пустошь'\n", "\\item 'пустошь'\n", "\\item 'пустошь'\n", "\\item 'пустошь'\n", "\\item 'пустошь'\n", "\\item 'пустошь'\n", "\\item 'пустошь'\n", "\\item 'пустошь'\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 'море'\n", "2. 'море'\n", "3. 'море'\n", "4. 'море'\n", "5. 'море'\n", "6. 'море'\n", "7. 'море'\n", "8. 'море'\n", "9. 'море'\n", "10. 'море'\n", "11. 'море'\n", "12. 'море'\n", "13. 'пустошь'\n", "14. 'пустошь'\n", "15. 'пустошь'\n", "16. 'пустошь'\n", "17. 'пустошь'\n", "18. 'пустошь'\n", "19. 'пустошь'\n", "20. 'пустошь'\n", "\n", "\n" ], "text/plain": [ " [1] \"море\" \"море\" \"море\" \"море\" \"море\" \"море\" \"море\" \n", " [8] \"море\" \"море\" \"море\" \"море\" \"море\" \"пустошь\" \"пустошь\"\n", "[15] \"пустошь\" \"пустошь\" \"пустошь\" \"пустошь\" \"пустошь\" \"пустошь\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# вектор номеров\n", "room = c(rep('море',12),rep('пустошь',8))\n", "room" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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    \n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 'россиянин'\n", "\\item 'россиянин'\n", "\\item 'россиянин'\n", "\\item 'россиянин'\n", "\\item 'россиянин'\n", "\\item 'россиянин'\n", "\\item 'россиянин'\n", "\\item 'россиянин'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\item 'иностранец'\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 'россиянин'\n", "2. 'россиянин'\n", "3. 'россиянин'\n", "4. 'россиянин'\n", "5. 'россиянин'\n", "6. 'россиянин'\n", "7. 'россиянин'\n", "8. 'россиянин'\n", "9. 'иностранец'\n", "10. 'иностранец'\n", "11. 'иностранец'\n", "12. 'иностранец'\n", "13. 'иностранец'\n", "14. 'иностранец'\n", "15. 'иностранец'\n", "16. 'иностранец'\n", "17. 'иностранец'\n", "18. 'иностранец'\n", "19. 'иностранец'\n", "20. 'иностранец'\n", "\n", "\n" ], "text/plain": [ " [1] \"россиянин\" \"россиянин\" \"россиянин\" \"россиянин\" \"россиянин\" \n", " [6] \"россиянин\" \"россиянин\" \"россиянин\" \"иностранец\" \"иностранец\"\n", "[11] \"иностранец\" \"иностранец\" \"иностранец\" \"иностранец\" \"иностранец\"\n", "[16] \"иностранец\" \"иностранец\" \"иностранец\" \"иностранец\" \"иностранец\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# вектор спортсменов \n", "sport = c(rep('россиянин',8),rep('иностранец',12))\n", "sport " ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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    \n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'пустошь'\n", "\\item 'пустошь'\n", "\\item 'море'\n", "\\item 'пустошь'\n", "\\item 'море'\n", "\\item 'пустошь'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'море'\n", "\\item 'пустошь'\n", "\\item 'пустошь'\n", "\\item 'море'\n", "\\item 'пустошь'\n", "\\item 'пустошь'\n", "\\item 'море'\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 'море'\n", "2. 'море'\n", "3. 'море'\n", "4. 'море'\n", "5. 'пустошь'\n", "6. 'пустошь'\n", "7. 'море'\n", "8. 'пустошь'\n", "9. 'море'\n", "10. 'пустошь'\n", "11. 'море'\n", "12. 'море'\n", "13. 'море'\n", "14. 'море'\n", "15. 'пустошь'\n", "16. 'пустошь'\n", "17. 'море'\n", "18. 'пустошь'\n", "19. 'пустошь'\n", "20. 'море'\n", "\n", "\n" ], "text/plain": [ " [1] \"море\" \"море\" \"море\" \"море\" \"пустошь\" \"пустошь\" \"море\" \n", " [8] \"пустошь\" \"море\" \"пустошь\" \"море\" \"море\" \"море\" \"море\" \n", "[15] \"пустошь\" \"пустошь\" \"море\" \"пустошь\" \"пустошь\" \"море\" " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Достаточно перемешать либо комнаты либо спортсменов\n", "sample(room)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
    sportroom
    россиянинморе
    россиянинморе
    россиянинпустошь
    россиянинпустошь
    россиянинморе
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    \n" ], "text/latex": [ "\\begin{tabular}{r|ll}\n", " sport & room\\\\\n", "\\hline\n", "\t россиянин & море \\\\\n", "\t россиянин & море \\\\\n", "\t россиянин & пустошь \\\\\n", "\t россиянин & пустошь \\\\\n", "\t россиянин & море \\\\\n", "\t россиянин & море \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "sport | room | \n", "|---|---|---|---|---|---|\n", "| россиянин | море | \n", "| россиянин | море | \n", "| россиянин | пустошь | \n", "| россиянин | пустошь | \n", "| россиянин | море | \n", "| россиянин | море | \n", "\n", "\n" ], "text/plain": [ " sport room \n", "1 россиянин море \n", "2 россиянин море \n", "3 россиянин пустошь\n", "4 россиянин пустошь\n", "5 россиянин море \n", "6 россиянин море " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Перемешаем комнаты и соединим вектора в табличку\n", "df = data.frame('sport'=sport, 'room' = sample(room))\n", "head(df)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
    sportroom
    россиянинморе
    россиянинморе
    россиянинпустошь
    россиянинпустошь
    россиянинморе
    россиянинморе
    россиянинморе
    россиянинморе
    \n" ], "text/latex": [ "\\begin{tabular}{r|ll}\n", " sport & room\\\\\n", "\\hline\n", "\t россиянин & море \\\\\n", "\t россиянин & море \\\\\n", "\t россиянин & пустошь \\\\\n", "\t россиянин & пустошь \\\\\n", "\t россиянин & море \\\\\n", "\t россиянин & море \\\\\n", "\t россиянин & море \\\\\n", "\t россиянин & море \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "sport | room | \n", "|---|---|---|---|---|---|---|---|\n", "| россиянин | море | \n", "| россиянин | море | \n", "| россиянин | пустошь | \n", "| россиянин | пустошь | \n", "| россиянин | море | \n", "| россиянин | море | \n", "| россиянин | море | \n", "| россиянин | море | \n", "\n", "\n" ], "text/plain": [ " sport room \n", "1 россиянин море \n", "2 россиянин море \n", "3 россиянин пустошь\n", "4 россиянин пустошь\n", "5 россиянин море \n", "6 россиянин море \n", "7 россиянин море \n", "8 россиянин море " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# осталось только сделать срез по россиянам \n", "df[df$sport == 'россиянин',]" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "FALSE" ], "text/latex": [ "FALSE" ], "text/markdown": [ "FALSE" ], "text/plain": [ "[1] FALSE" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# И понять все ли они на море \n", "sum(df[df$sport == 'россиянин',]$room == 'море') == 8" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.003" ], "text/latex": [ "0.003" ], "text/markdown": [ "0.003" ], "text/plain": [ "[1] 0.003" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# объединяем всё это в цикл!\n", "n_obs = 1000\n", "\n", "# комнаты\n", "room = c(rep('море',12),rep('пустошь',8))\n", "# спортсмены\n", "sport = c(rep('россиянин',8),rep('иностранец',12))\n", "\n", "\n", "m = 0\n", "for(i in 1:n_obs){\n", " df = data.frame('sport'=sport, 'room' = sample(room))\n", " # если море встретилось у каждого россиянина, делаем плюс один\n", " if(sum(df[df$sport == 'россиянин',]$room == 'море') == 8){\n", " m = m + 1\n", " }\n", " \n", "}\n", "\n", "m/n_obs" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.003952" ], "text/latex": [ "0.003952" ], "text/markdown": [ "0.003952" ], "text/plain": [ "[1] 0.003952" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Можно избавиться от всяких табличек. Это довольно сильно ускорит работу кода.\n", "# Просто будем считать что первые 8 позиций вектора относятся к россиянам\n", "\n", "n_obs = 10^6\n", "\n", "# комнаты\n", "room = c(rep('море',12),rep('пустошь',8))\n", "\n", "m = 0\n", "for(i in 1:n_obs){\n", " if(sum(sample(room)[1:8] == 'море') == 8){\n", " m = m + 1\n", " }\n", "}\n", "\n", "m/n_obs" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.00392950702548226" ], "text/latex": [ "0.00392950702548226" ], "text/markdown": [ "0.00392950702548226" ], "text/plain": [ "[1] 0.003929507" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Теоретическая вероятность: \n", "factorial(12)*factorial(12)*factorial(8)/(factorial(8)*factorial(4)*factorial(20))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.3 Шнур\n", "\n", "На шнуре длиной $1$ м случайным образом делают два разреза. С какой вероятностью хотя бы один из получившихся кусков будет длиннее $0.5 м$?" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.677471707575023" ], "text/latex": [ "0.677471707575023" ], "text/markdown": [ "0.677471707575023" ], "text/plain": [ "[1] 0.6774717" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "0.940757564269006" ], "text/latex": [ "0.940757564269006" ], "text/markdown": [ "0.940757564269006" ], "text/plain": [ "[1] 0.9407576" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X1 = runif(1,min = 0, max = 1) # первый надрез \n", "X2 = runif(1,min = 0, max = 1) # второй надрез\n", "X1 \n", "X2" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "750250" ], "text/latex": [ "750250" ], "text/markdown": [ "750250" ], "text/plain": [ "[1] 750250" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_obs <- 10^6 # чисор шнуров для кромсания\n", "\n", "m <- 0 # сюда будем записывать правильно покромсаное количество\n", "for(i in 1:n_obs){\n", " X1 = runif(1,min = 0, max = 1) # симулируем первый разрез \n", " X2 = runif(1,min = 0, max = 1) # симулируем второй разрез \n", " \n", " # смотримна длины всех частичек шнура \n", " if(X2 > X1){\n", " \n", " # возможны 2 ситуации, когда X2 > X1 и наоборот\n", " m = m + 1*((1 - X2 > 0.5)|(X2 - X1 > 0.5)|(X1 - 0 > 0.5)) # если хотя бы один кусок длиннее 0.5, получаем 1\n", " }else{\n", " m = m + 1*((1 - X1 > 0.5)|(X1 - X2 > 0.5)|(X2 - 0 > 0.5)) \n", " }\n", "}\n", "\n", "m # посмотрим сколько шнуров были искромсаны удачнл" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.75025" ], "text/latex": [ "0.75025" ], "text/markdown": [ "0.75025" ], "text/plain": [ "[1] 0.75025" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m/n_obs" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "# теоретическую искать мне лень" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.4 Колода карт\n", "\n", "Лера довольно азартна. Она берёт карты из хорошо перемешанной колоды с 36 картами до тех пор, пока не возьмёт даму пик. Сколько в среднем бубновых карт она наберёт? Допустим, что каждая карта приносит Лере выигрыш согласно достоинству: шестёрка - 6 рублей, ..., десятка - 10 рублей, валет - 11 рублей, дама - 12 рублей и т.д. Какова вероятность того, что Лера наберёт меньше $100$ очков? Каков её средний выигрыш? " ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "n <- 10^6\n", "dost <- factor(c(6:10,\"валет\",\"дама\",\"король\",\"туз\")) # возможные достоинства карт\n", "mast <- factor(c(\"бубны\",\"черви\",\"пики\",\"крести\")) # возможные масти" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
    Var1Var2
    6 бубны
    7 бубны
    8 бубны
    9 бубны
    10 бубны
    валетбубны
    \n" ], "text/latex": [ "\\begin{tabular}{r|ll}\n", " Var1 & Var2\\\\\n", "\\hline\n", "\t 6 & бубны\\\\\n", "\t 7 & бубны\\\\\n", "\t 8 & бубны\\\\\n", "\t 9 & бубны\\\\\n", "\t 10 & бубны\\\\\n", "\t валет & бубны\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "Var1 | Var2 | \n", "|---|---|---|---|---|---|\n", "| 6 | бубны | \n", "| 7 | бубны | \n", "| 8 | бубны | \n", "| 9 | бубны | \n", "| 10 | бубны | \n", "| валет | бубны | \n", "\n", "\n" ], "text/plain": [ " Var1 Var2 \n", "1 6 бубны\n", "2 7 бубны\n", "3 8 бубны\n", "4 9 бубны\n", "5 10 бубны\n", "6 валет бубны" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# табличка соответствий между кодом карты, мастью и очками за ее получение\n", "koloda <- expand.grid(dost,mast) # узнаешь ли ты Дездемона, декартово произведение?\n", "head(koloda)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
    dostmastidvalue
    6 бубны1 6
    7 бубны2 7
    8 бубны3 8
    9 бубны4 9
    10 бубны5 10
    валетбубны6 11
    дама бубны7 12
    \n" ], "text/latex": [ "\\begin{tabular}{r|llll}\n", " dost & mast & id & value\\\\\n", "\\hline\n", "\t 6 & бубны & 1 & 6 \\\\\n", "\t 7 & бубны & 2 & 7 \\\\\n", "\t 8 & бубны & 3 & 8 \\\\\n", "\t 9 & бубны & 4 & 9 \\\\\n", "\t 10 & бубны & 5 & 10 \\\\\n", "\t валет & бубны & 6 & 11 \\\\\n", "\t дама & бубны & 7 & 12 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "dost | mast | id | value | \n", "|---|---|---|---|---|---|---|\n", "| 6 | бубны | 1 | 6 | \n", "| 7 | бубны | 2 | 7 | \n", "| 8 | бубны | 3 | 8 | \n", "| 9 | бубны | 4 | 9 | \n", "| 10 | бубны | 5 | 10 | \n", "| валет | бубны | 6 | 11 | \n", "| дама | бубны | 7 | 12 | \n", "\n", "\n" ], "text/plain": [ " dost mast id value\n", "1 6 бубны 1 6 \n", "2 7 бубны 2 7 \n", "3 8 бубны 3 8 \n", "4 9 бубны 4 9 \n", "5 10 бубны 5 10 \n", "6 валет бубны 6 11 \n", "7 дама бубны 7 12 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "koloda$id <- 1:36\n", "koloda$value <- rep(6:14,4)\n", "\n", "# приемлимые названия столбцов\n", "colnames(koloda) <- c(\"dost\",\"mast\",\"id\",\"value\")\n", "\n", "head(koloda,7)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
    dostmastidvalue
    3210 крести32 10
    33валет крести33 11
    34дама крести34 12
    35королькрести35 13
    36туз крести36 14
    \n" ], "text/latex": [ "\\begin{tabular}{r|llll}\n", " & dost & mast & id & value\\\\\n", "\\hline\n", "\t32 & 10 & крести & 32 & 10 \\\\\n", "\t33 & валет & крести & 33 & 11 \\\\\n", "\t34 & дама & крести & 34 & 12 \\\\\n", "\t35 & король & крести & 35 & 13 \\\\\n", "\t36 & туз & крести & 36 & 14 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "| | dost | mast | id | value | \n", "|---|---|---|---|---|\n", "| 32 | 10 | крести | 32 | 10 | \n", "| 33 | валет | крести | 33 | 11 | \n", "| 34 | дама | крести | 34 | 12 | \n", "| 35 | король | крести | 35 | 13 | \n", "| 36 | туз | крести | 36 | 14 | \n", "\n", "\n" ], "text/plain": [ " dost mast id value\n", "32 10 крести 32 10 \n", "33 валет крести 33 11 \n", "34 дама крести 34 12 \n", "35 король крести 35 13 \n", "36 туз крести 36 14 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tail(koloda,5)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
      \n", "\t
    1. 4
    2. \n", "\t
    3. 5
    4. \n", "\t
    5. 9
    6. \n", "\t
    7. 29
    8. \n", "
    \n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 4\n", "\\item 5\n", "\\item 9\n", "\\item 29\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 4\n", "2. 5\n", "3. 9\n", "4. 29\n", "\n", "\n" ], "text/plain": [ "[1] 4 5 9 29" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Возьмём 4 карты из колоды:\n", "z <- sample(1:36,4) # коды вытянутых карт\n", "z" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
    dostmastidvalue
    49 бубны 4 9
    510 бубны 5 10
    9туз бубны 9 14
    297 крести29 7
    \n" ], "text/latex": [ "\\begin{tabular}{r|llll}\n", " & dost & mast & id & value\\\\\n", "\\hline\n", "\t4 & 9 & бубны & 4 & 9 \\\\\n", "\t5 & 10 & бубны & 5 & 10 \\\\\n", "\t9 & туз & бубны & 9 & 14 \\\\\n", "\t29 & 7 & крести & 29 & 7 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "| | dost | mast | id | value | \n", "|---|---|---|---|\n", "| 4 | 9 | бубны | 4 | 9 | \n", "| 5 | 10 | бубны | 5 | 10 | \n", "| 9 | туз | бубны | 9 | 14 | \n", "| 29 | 7 | крести | 29 | 7 | \n", "\n", "\n" ], "text/plain": [ " dost mast id value\n", "4 9 бубны 4 9 \n", "5 10 бубны 5 10 \n", "9 туз бубны 9 14 \n", "29 7 крести 29 7 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "koloda[z,]" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " num [1:1000000] 0 0 0 0 0 0 0 0 0 0 ...\n" ] } ], "source": [ "s <- rep(0, times = n) # s - это вектор из n штук нулей\n", "str(s)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "for (i in 1:n) {\n", " z <- sample(1:36,36) # тасуем колоду\n", " \n", " # 25 - код пиковой дамы в таблице koloda\n", " k.dama <- which(z==25) # координата дамы\n", " \n", " do.damy <- z[1:(k.dama-1)] # коды карт до дамы\n", " s[i] <- sum(koloda$value[do.damy]) # полученный выигрыш в i-ом опыте\n", "\n", "}" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/html": [ "174.505683" ], "text/latex": [ "174.505683" ], "text/markdown": [ "174.505683" ], "text/plain": [ "[1] 174.5057" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "102.877708428631" ], "text/latex": [ "102.877708428631" ], "text/markdown": [ "102.877708428631" ], "text/plain": [ "[1] 102.8777" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mean(s) # средний выигрыш за n опытов\n", "sd(s) # стандартное отклонение выигрыша за одну партию" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.705953" ], "text/latex": [ "0.705953" ], "text/markdown": [ "0.705953" ], "text/plain": [ "[1] 0.705953" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Как часто выигрыш оказывался больше 100? \n", "sum(s > 100)/n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Надеюсь, что за сегодня мы многое поняли! На пока что это всё. " ] } ], "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 }