{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Введение в анализ данных"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2020-05-07T14:52:27.061143Z",
"start_time": "2020-05-07T14:52:26.390010Z"
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.stats as sps\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import animation as animation\n",
"\n",
"sns.set(font_scale=1.6, palette='summer')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Закон больших чисел\n",
"\n",
"**Формулировка.**\n",
"\n",
"Пусть $\\xi_1, ..., \\xi_n$ — независимые случайные величины из некоторого распределения, причем $\\mathsf{E}\\xi_i = a$. Тогда выполнена сходимость $$\\frac{\\xi_1 + ... + \\xi_n}{n} \\stackrel{п.н.}{\\longrightarrow} a.$$ \n",
"\n",
"*Замечание 1.* Закон больших чисел имеет несколько формулировок. Данная формулировка часто называется *усиленным законом больших чисел*. В частности, усиленной она является, поскольку в отличии от \"простой\" версии она не требует условия на дисперсии и утверждает о более сильной сходимости \"почти наверное\".\n",
"\n",
"*Замечание 2.* Последовательность случайных величин $\\xi_1, \\xi_2, ...$ сходится почти наверное к случайной величине $\\xi$, если $\\mathsf{P}\\big(\\big\\{ \\omega \\in \\Omega\\:\\big|\\: \\xi_n(\\omega) \\to \\xi(\\omega)\\big\\}\\big) = 1$\n",
"\n",
"---\n",
"\n",
"### 1. Визуализация\n",
"\n",
"Убедимся в справедливости ЗБЧ, сгенерировав набор из случайных величин $\\xi_1, ..., \\xi_{1000}$ и посчитав по нему среднее в зависимости от размера набора, то есть величины $S_{n} = \\frac{1}{n}\\sum\\limits_{i=1}^n \\xi_i$ для $1 \\leqslant n \\leqslant 1000$.\n",
"\n",
"Для примера рассмотрим бернуллиевское распределение."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2020-05-07T14:52:27.070628Z",
"start_time": "2020-05-07T14:52:27.063447Z"
}
},
"outputs": [],
"source": [
"size = 1000 # количество случайных величин\n",
"samples = sps.bernoulli(p=0.5).rvs(size=size)\n",
"cum_means = samples.cumsum() / (np.arange(size) + 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Построим график"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2020-05-07T14:52:27.432295Z",
"start_time": "2020-05-07T14:52:27.072762Z"
}
},
"outputs": [
{
"data": {
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\n",
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