HW_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "36b600c3",
   "metadata": {},
   "source": [
    "# Задание №2\n",
    "##  Вопрос №1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "184cf1e7",
   "metadata": {},
   "source": [
    "Пусть задано вероятностное пространство $(\\Omega ,{\\mathcal {F}},\\mathbb {P} )$, и на нём определена случайная величина $ ξ:\\Omega \\to \\mathbb {R}$. Тогда:\n",
    "$\\forall x\\in {\\mathbb {R}} : \\{\\omega \\in \\Omega : ξ(\\omega) \\leq x\\} \\in {\\mathcal {F}}$\n",
    "\n",
    "Тогда вероятность попадания в отрезок до $x$ включительно:\n",
    "\n",
    "$${P}(ξ \\leq x) = {P}(\\{\\omega \\in \\Omega : ξ(\\omega) \\leq x\\}) = F_{ξ}(x)$$\n",
    "\n",
    "Функция $F_{ξ}(x)$ называют функция распределения случайной величины, часто обозначают, как CDF. \n",
    "Множество отрезков от минус бесконечности до $x$ - называют Борелевым множеством и обозначают ${\\mathcal {B}}$.\n",
    "\n",
    "\n",
    "Функция распределения $F_{ξ}(x)$ любой случайной величины удовлетворяет следующим трем свойствам:\n",
    "\n",
    "1) $F_{ξ}$ — функция неубывающая;\n",
    "2) $\\lim _{x\\to -\\infty }F_{ξ}(x)=0,\\;\\lim _{x\\to \\infty }F_{ξ}(x)=1$;\n",
    "3) $F_{ξ}$ непрерывна справа.\n",
    "\n",
    "Бывают два типа распределение случайной величины дискретное и непрерывное.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ce3f33f",
   "metadata": {},
   "source": [
    "## Вопрос №2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f7a8cee",
   "metadata": {},
   "source": [
    "Из-за наличие центральной предельной теоремы, которая утверждает, что не важно, как была первоначально распределена случайная величина $X$. Для нее будет выполняться предельное соотношение:\n",
    "\n",
    "Пусть $X_{1},\\ldots ,X_{n},\\ldots$  есть бесконечная последовательность независимых одинаково распределённых случайных величин, имеющих конечное математическое ожидание $\\mu$  и дисперсию $\\sigma ^{2}$. \n",
    "\n",
    "Тогда\n",
    "\n",
    "$${\\frac  {\\sum \\limits _{i=1}^{n}X_{i}-\\mu n}{\\sigma {\\sqrt  n}}}\\to N(0,1)$$ по распределению при $n\\to \\infty$ ,\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8883685",
   "metadata": {},
   "source": [
    "## Вопрос №3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "159660a0",
   "metadata": {},
   "source": [
    "Количество событий в гистограммы являются функцией плотности распределения случайной величины. $p(x)\\cdot N $, где $p(x)$ - плотность распределения случайной величины в точке x, N - количество наблюдаемых значений случайной величины попавшая в диапазон вокруг x. В одном биме плотность распределения равномерная, но должна быть отнормировано не по вероятности 1, а по той доли, которая занимает диапазон значений x от числа общих наблюдений."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "326d8b75",
   "metadata": {},
   "source": [
    "## Вопрос№4"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f110303",
   "metadata": {},
   "source": [
    "Рост людей распределен по нормальному закону распределения. Доход людей по логнормальному закону распределению.\n",
    "\n",
    "Нормальное распределение имеет \"тонкие хвосты\", то есть среднее значение практически не измениться от визита самого высокого человека на земле, так и его рост так же не будет значительно отклоняться от среднего значения выборки. \n",
    "Вклад самого высокого человека в среднее будет зависить от n:\n",
    "\n",
    "$$\\frac{\\sum \\limits _{i=1}^{n}x_{i}}{n} $$\n",
    "\n",
    "$$\\frac{x_{(n)}}{n} $$\n",
    "\n",
    "${x_{(n)}} $ - максимальное значение вариационного ряда.\n",
    "\n",
    "В случае доходов, в силу \"толстых\" хвостов влияние, самого богатого будет значительным:\n",
    "1) Его богатство может существенно отличаться от среднего;\n",
    "\n",
    "2) Рост параметров распределения(которые уже зависят от квадратов значений выборки) будет вызывать степенной рост среднего значения:\n",
    "\n",
    "$${\\mathbb  {E}}[X]=e^{{\\mu +{\\sigma ^{2} \\over 2}}}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6363bd9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.stats as sts\n",
    "import math\n",
    "%matplotlib inline\n",
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0e1df266",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.0968490300507443\n",
      "Процент отклонения среднего 90.65525078706999\n"
     ]
    }
   ],
   "source": [
    "a_1 = np.random.normal(size = 10)\n",
    "print(sum(a_1))\n",
    "a_2 = np.append(a_1, [100])\n",
    "mu_1 = np.log(((sum(a_1))**2) / ((len(a_1))**(3/2) * sum(a_1**2)))\n",
    "sigma_1 = 4/3 * np.log(((len(a_1))**2)*(sum(a_1**2)) / (sum(a_1))**2)\n",
    "Mean_1 = np.exp(mu_1 + sigma_1/2)\n",
    "mu_2 = np.log(((sum(a_2))**2) / ((len(a_2))**(3/2) * sum(a_2**2)))\n",
    "sigma_2 = 4/3 * np.log(((len(a_2))**2)*(sum(a_2**2)) / (sum(a_2))**2)\n",
    "Mean_2 = np.exp(mu_2 + sigma_2/2)\n",
    "print('Процент отклонения среднего', (Mean_2 - Mean_1)/Mean_1*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5fa2f15",
   "metadata": {},
   "source": [
    "## Вопрос №5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ac88f9b",
   "metadata": {},
   "source": [
    "Алгоритм будет выбирать значения от 0 до 3-х успехов k = (0, 1, 2, 3), с вероятностью успеха в единичном испытании $p = \\frac {1}{2}$ с вероятностью распределенной по биномиальному закону распределения.\n",
    "\n",
    "\n",
    "Функция вероятности задаётся формулой:\n",
    "\n",
    "$p_{Y}(k)\\equiv {\\mathbb  {P}}(Y=k)={\\binom  {n}{k}}\\,p^{k}q^{{n-k}},\\ \\ k=0,\\ldots ,3,$\n",
    "где\n",
    "\n",
    "${{\\binom {n}{k}}=C_{n}^{k}={\\frac {n!}{(n-k)!\\,k!}}}$ — биномиальный коэффициент.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "394db7be",
   "metadata": {},
   "source": [
    "## Задача №1 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57c18fef",
   "metadata": {},
   "source": [
    "Для точечной оценки параметра d можно воспользоваться двумя методами:\n",
    "1) Методом моментов:\n",
    "$$ \\frac{d}{2} = \\frac{1}{n}\\sum \\limits _{i=1}^{n}x_{i}$$\n",
    "Откуда:\n",
    "$$ d = \\frac{2}{n}\\sum \\limits _{i=1}^{n}x_{i}$$\n",
    "2) Метод максимального правдоподобия:\n",
    "$$ d = x_{(n)}$$\n",
    "3) Интервальная оценка дает следующую формулу:\n",
    "$$\\frac{2\\bar x}{1+\\frac{1}{\\sqrt{12n}}} \\leq \\bar d \\leq  \\frac{2\\bar x}{1-\\frac{1}{\\sqrt{12n}}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "97a86f37",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.978055512723744\n",
      "5.025164026155448\n",
      "4.979705740095643 5.071459909352708\n"
     ]
    }
   ],
   "source": [
    "a_3 = np.random.uniform(low =0 , high = 5, size = 1000)\n",
    "print(max(a_3))\n",
    "print(2*np.mean(a_3))\n",
    "print(2*np.mean(a_3)/(1+1/np.sqrt(12*len(a_3))),2*np.mean(a_3)/(1-1/np.sqrt(12*len(a_3))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5d26b64",
   "metadata": {},
   "source": [
    "## Задача №2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97faf298",
   "metadata": {},
   "source": [
    "Для вычисления воспользуемся формулой Муавра — Лапласа:\n",
    "$$P({\\frac  {312-np}{{\\sqrt  {npq}}}}\\leq \\frac  {\\mu_{n}-np}{{\\sqrt  {npq}}} \\leq {\\frac  {576-np}{{\\sqrt  {npq}}}})=$$\n",
    "$$=P({\\frac  {312-288}{12}}\\leq \\frac  {\\mu_{n}-np}{{\\sqrt  {npq}}}\\leq {\\frac  {576-288}{12}}) = Ф(24) - Ф(2) = 0.0227$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0ca77c73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02275013194817921"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sts.norm.cdf(24)-sts.norm.cdf(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db6f614f",
   "metadata": {},
   "source": [
    "## Задача №3, 4"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41307a72",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b39132b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import simps\n",
    "def integrateS(func, a, b, numPoints = 1000):\n",
    "    x = np.linspace(a,b, numPoints, endpoint=True)\n",
    "    return simps(x = x, y = func(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "4c77da6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "convolute = lambda f, g, a, b:  np.vectorize(lambda x:integrateS(lambda y: f(x-y)*g(y), a, b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "7a6d1752",
   "metadata": {},
   "outputs": [
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   "source": [
    "wStep = 4 # Ширина ступеньки\n",
    "sigma = 0.5 # Стандартное отклонение Гауссианы\n",
    "sigma_f = 0.8\n",
    "mu_cauchy = 0 \n",
    "gamma = 1\n",
    "\n",
    "# ступенька\n",
    "f = lambda x: 1/wStep if (-wStep / 2 <= x <= wStep / 2) else 0.0 # нормировка на единицу\n",
    "#f = lambda x : 1/np.sqrt(2*math.pi)/sigma_f*np.exp(-x*x/2/sigma_f/sigma_f)\n",
    "#f = lambda x : 1/math.pi * gamma/ ((x-mu_cauchy)*(x-mu_cauchy)+gamma*gamma)\n",
    "f = np.vectorize(f)\n",
    "\n",
    "# Функция Гаусса\n",
    "#g = lambda x : 1/np.sqrt(2*math.pi)/sigma*np.exp(-x*x/2/sigma/sigma)\n",
    "g = lambda x: 1/wStep if (-wStep / 2 <= x <= wStep / 2) else 0.0\n",
    "g = np.vectorize(g)\n",
    "\n",
    "# Plot plot = new Plot(title: \"Convolution test plot\", showLegend: true)\n",
    "\n",
    "\n",
    "# автоматическое определение окна интегрирования и отрисовки\n",
    "wind = max(2*wStep, 4*sigma)\n",
    "x = np.linspace(-wind, wind, 500)\n",
    "\n",
    "traces = [\n",
    "    go.Scatter(x = x, y = f(x), name = \"f(x)\"),\n",
    "    go.Scatter(x = x, y = g(x), name = \"g(x)\"),\n",
    "    go.Scatter(x = x, y = convolute(f,g, -wind, wind)(x), name = \"convolution\")\n",
    "]\n",
    "\n",
    "go.Figure(traces)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "caa128ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8333136089442954 0.6739635733548864 1.3777605377859574\n"
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   ],
   "source": [
    "wStep_a = 0\n",
    "wStep_b = 2\n",
    "# Ширина ступеньки\n",
    "sigma = 0.5\n",
    "sigma_f = 0.8\n",
    "mu_cauchy = 0 \n",
    "gamma = 1\n",
    "wind = max(2*wStep_a, 4*sigma, 2*wStep_b)\n",
    "#f = lambda x : 1/np.sqrt(2*math.pi)/sigma_f*np.exp(-x*x/2/sigma_f/sigma_f)\n",
    "#f = lambda x: 1/(wStep_b - wStep_a) if (wStep_a <= x <= wStep_b) else 0.0 # нормировка на единицу\n",
    "f = lambda x : 1/math.pi * gamma/ ((x-mu_cauchy)*(x-mu_cauchy)+gamma*gamma)\n",
    "f = np.vectorize(f)\n",
    "#g = lambda x : 1/np.sqrt(2*math.pi)/sigma*np.exp(-x*x/2/sigma/sigma)\n",
    "g = lambda x: 1/(wStep_b - wStep_a) if (wStep_a <= x <= wStep_b) else 0.0\n",
    "g = np.vectorize(g)\n",
    "sample = convolute(f, g, -wind, wind)\n",
    "a = -wind\n",
    "b = wind\n",
    "N = 100\n",
    "delta_x = (b-a) / (N-1)\n",
    "x = np.linspace(a, b, N)\n",
    "y = sample(x)\n",
    "mu_gen = np.sum(y*x*delta_x)\n",
    "sigma_gen = np.sqrt(np.sum(y*((x-mu_gen)**2))*delta_x)\n",
    "print(np.sum(y*delta_x), mu_gen, sigma_gen)\n",
    "go.Figure(go.Scatter(x = x, y = y, name = \"convolution\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "0415ee9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средене значение выборки n = 10: -0.008323232323231998\n",
      "Средене значение N(sigma, mu) n = 10: 0.4356861369702105\n",
      "Cреднеквадратическое отклонение выборки n = 10: 0.738739373564786\n",
      "Cреднеквадратическое отклонение N(sigma, mu) n = 10: 0.6739635733548864\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средене значение выборки n = 100: 0.6722846414230265\n",
      "Средене значение N(sigma, mu) n = 100: 0.13777605377859575\n",
      "Cреднеквадратическое отклонение выборки n = 100: 0.12434505764077267\n",
      "Cреднеквадратическое отклонение N(sigma, mu) n = 100: 0.6739635733548864\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средене значение выборки n = 1000: 0.6741228090727991\n",
      "Средене значение N(sigma, mu) n = 1000: 0.04356861369702106\n",
      "Cреднеквадратическое отклонение выборки n = 1000: 0.01282297215734765\n",
      "Cреднеквадратическое отклонение N(sigma, mu) n = 1000: 0.6739635733548864\n"
     ]
    },
    {
     "data": {
      "image/png": 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r8B8CXGBmH0avewALzew1wN19v+pvcPdzsyznnm0rU0REGkquwX9SrFWIiEje5BT87v5B3IWIiEh+6A5cIiIpo+AXEUkZBb+ISMoo+EVEUkbBLyKSMgp+EZGUUfCLiKSMgl9EJGUU/CIiKaPgFxFJGQW/iEjKKPhFRFJGwS8ikjIKfhGRlFHwi4ikTK43YhFplkpGTUu6BJG80x6/iEjKKPhFRFJGwS8ikjJq4xfJo2zHFBbdfEoClUiaaY9fRCRlFPwiIimj4BcRSRkFv4hIysQW/GZ2r5ktN7MFGeM6mdl0M3s7euwY1/pFRCS7OPf47wNOqjZuFDDD3fcEZkSvRUQkj2ILfnd/AVhRbfRgYEz0fAxwelzrFxGR7PLdxt/V3ZcCRI875nn9IiKp12gP7prZSDObZWazSktLky5HRKTZyHfwLzOzbgDR4/KaZnT30e7e3937FxcX561AEZHmLt/BPxW4MHp+ITAlz+sXEUm9OE/nHA/MBPY2s8VmNgK4GTjezN4Gjo9ei4hIHsXWSZu7n1vDpIFxrVMkH4wqetlS2rL+v+OWemeWo8tSpGlQ75wiOdiFUoYWPc/B9iZfLXifdrZ+i3mWeCfmVe3O81V9mVJ5OOtpnUClInVT8IvU4rCC17mo8CkGFswBYIH3ZFLlkcz3XnzqOwBgQIl9Qt+CdznA3mZQi1e5qmgcj1QexX2VJ/Khd03wJxDZkoJfJIvuVso1RWM4vnAOn/oO/LnyNMZtHMgSutT8pkoA5wB7mwuK/s55hdMZXvg0d1Seyp82DuYLWuarfJFaKfhFMhRSycjCaVxe9ChVGDdWDGNM5YmU0yLHJRhzfC/mVOzFjQznpy3Gc0XRJIYUvMjPN36LF6r6xlq/SC4a7QVcIvnWiTWMaXEzP2nxEM9X9eW4L27hrsqvb0Xob66UjlxZ8T+cW/4zymnB2Ja/5sqiCRRQ1cCVi2wd7fGLAF+197ij5W10YQ0/qhjJXysHNNiyZ1btyynlN3F90V+4vGgy+9n7XFFxKatp22DrENka2uOX1Dux4BUeaXkdjnFm+TUNGvqbfEFLfrxxJFdVjODwggVMaXk13a3GC9dFYqXgl1Q7q/B5/tTi97zmPTn1ixtY4L1iXJsxrnIg55RfTXtbxyMtr2MPWxzj+kSyU/BLer18B7e0uJOXqvpwfvkoVrJDXlY7x/fi7PKrKcCZ0PKXsOTfeVmvyCYKfkmnmbfDUz/hqcqD+HbFD/N+sdV/fFfOKr+Gdb4djDlN4S95peCX9JkzFv52FfQezKUVl2/zWTv19aF3ZWj5L2C7DvDAmVD6ViJ1SPoo+CVdFjwKUy+HPY6DM+6mksJEy/mEznD+ZCgogrGDYeWiROuRdFDwS3q8+ww8OhJ6HArfuB+KGsmVtJ13h/MnQcV6GHs6lOnGQxIvBb+kw7I34OELoMteMOxhaNkm6Yo213VfOG8irP0EHjo3fAiIxETBL83f2k9g3DegVVsYPgFat0+6ouy694cz74LFs2DSJVClK3wlHgp+ad7K18H4c+DzFXDuQ9C+e9IV1W6fU+GE6+GNyfDML5OuRpopddkgzZc7TP4uLJ0H54yDnfslXVFuDrsMVrwHL94Wmqb6DUu6ImlmtMcvzdcLt8AbU+D4X8Leg5KuJndmMOg30PMoeOx7sHh20hVJM6Pgl+bpzSfg2Rtgv7PDHnRTU9gCzroP2nWFh4eH4xQiDUTBL81P6VvhtM1u/eDU34c96KZo+85wznjYsBoePg82fpF0RdJMKPiledmwGh4aBi1awzkPQovtkq6ofnbqA0PugMWvwpM/TroaaSYU/NJ8VFXBpO/Civdh6JjGfwZPrnoPhiO/D7Pvg9ljkq5GmgEFvzQfL94Kb02DE2+EkiOSrqZhHXs19BoAT/wQPtbBXqkfBb80D+/MgGdugK8OhUMuSbqahldQCGfeC227hiuQ132adEXShCn4pelb+QFMHAE79m7aB3Prsn1nOPt+WFcKj3wLqiqTrkiaKAW/NG0VG2DCBaF9/+z7oeX2SVcUr533h6/fCu8/H77hiGwDBb80bU/+CJbODWe+dN496WryY//z4MBvhmMaCx9PuhppghLpssHMFgFrgUpgo7v3T6IOaeJmjwk3VfnaD+ErJyddTX4N+g0snR+6pCj+CnTZI+mKpAlJco//GHfvp9CXbbJ4djjDpdcxcMxVSVeTf0Wt4BtjwxW+Dw+HL8qSrkiaEDX1SNNTVgoTzoe2O8FZ94YzXtKow67h5//0PzDl0tApnUgOkgp+B/5uZrPNbGS2GcxspJnNMrNZpaW6I5FEKjfCIxfB55/BOQ9Am05JV5SsXgPguGtDN87//P8JFyNNRVLBf4S7HwAMAi41s6Oqz+Duo929v7v3Ly4uzn+F0jg9fQ0s+kc4bbNb36SraRwOvzxc3fv0NfDec0lXI01AIsHv7kuix+XAJODgJOqQJmbeQzDzj3DwSOh7TtLVNB5mMPh26LI3/PWbocsKkVrkPfjNbHsza7fpOXACsCDfdUgT8/FsmHo5lHwNTrwp6Woan1bt4NxxoZ3/oWE62Cu1SmKPvyvwopnNA14Bprn7UwnUIU3F2k/goeGhb/qhY8KZLLKlTr1g6H1Q+iZMulj37JUa5T343f09d+8bDfu6+435rkGakIr1IfQ3rA5902/fOemKGrfdj4ETboQ3H4fnfpV0NdJI6Z670nhVVYULlD6eHc5Z36lP0hU1DYd+F5a/Di/8JlzNrOMhUo2CXxqvZ2+A1yeFe+b2Pi3papoOMzjlttB53ZTLoP2uza+baqkXXcAljdO/H4R//BYOuCCcrihbp6hl6LSuY0m4svezd5OuSBoRBb80Pm8/DY9dDj2PhlNubb7dLMdtu44wfAJYATxwBqxdlnRF0kgo+KVxWTwrdMdQvE/YY9UZPPXTqRcMmwBly+HBM8NBckk9Bb80HqX/gQeHQtsd4byJ0Lp90hU1D937hw/R5QvDGVIVG5KuSBKm4JfGYeUHcP+Q0OHa+ZPCOfvScPY4Dk7/c+juYuIIqKxIuiJJkIJfkrfqIxjzdSgvg/MeDc0T0vD2+wYM+t9wjv/EEaHDO0klnc4pyVr9cQj99avhwinQbb+kK8q7klHTso5fdPMpDb+yQ0ZCVQX87SooGAlDRkOhYiBt9BuX5Kz6EMYOhs9XwPmTw/1kJX6HXQpVG2H6L8LrIXfqIHrKKPglGaVvhTb98rJwILf7gbGvsqY961Q64orQodvT18AXa0MfSC3bJF2V5Ina+CX/Fs+Ge08KBxi/+QTsql65E3Hk9+Drv4O3p4fz/NevSrggyRcFv+TXW0/C2NNCN8Ij/qb+d5LW/yIY+pdw/cRfBoWzq6TZU/BLfrjDi7+D8edC5z3gW3/T2TuNxb5DYPhfw4H2u46FD2YmXZHETMEv8atYH3rZfPoa2Pd0uOhJ2KFb0lVJpt2Pge/MCBfNjTkV5tyfdEUSIwW/xKv0LbhrIMwbDwN+Cmf9RQcRG6sue4bwLzkCpl4Gky7RnbyaKQW/xMM97DWOHgBly2D4RBgwSh2uNXbbdQwX0R09CuY/DKOPhqXzk65KGpiCXxre6o9DW/7Uy0I/MZe8CHsel3RVkquCQjjmp3DBVChfF9r9n/0VbPwi6cqkgSj4peFUVcGr98Dth8B7z8EJN4QLs9Se3zT1/Bpc8lI4+Pv8zXDnUfDRK0lXJQ1AwS8N4/0X4K4BMO3KcDHW/8yEw/9f2HuUpmv7znDmXTDsr6G9/57jYeJ3wlXX0mTpyl2pn6Xz4dkb4T9PhVv8nXE3fPUsteU3gGxXGsfSf08u9joBLn0ZXrwNZt4Ob0yBQy8Jd0fbvksyNck2U/DLtvngn/CPW+Gd6dBqBzjuOjjkEmjROunKJC6t2sHAX0D/b8EzN8BLf4B/jYYDL4TDLoMOuyZdoeRIwS+527AGFjwCs8fA0rnQpgscezUc9G3YrkPS1f2X+uSJWfvuMOQOOPJKeOl38OrdYdh7EBzwzXBNgJr4GjUFv9SuYgO8+wy8MRkWPg4V62DHfeHkW6DfcJ2Tn2bFe8HpfwrXZ7xyJ8wdBwsfg/Y9oM8Q6H166HFVzX6NjoJftrTqQ3j32RD478yA8rXQugP0OQMO/CbscqD+meVLHXYNZ3AdezW8OQ3+/UA4DvDS76FDD9jzBNj9WCj5GrTeIelqBQW/fFEW7sW6ZA4sfjUMKxeFae26hS4Wep8OvY5Wn+1Su6JWYeegzxnhHgtvPRG+AcwdH5qCrBB2+ip0PygM3fqGfpt0I5i8S2SLm9lJwO+BQuBud785iTpSwR02rIY1S8Kw8n1Y8T6seBdK3/wy5CEEffeD4OCLwx5a8d7as5dt06YT7H9eGDaWw+JXwrfIxa+E7jtevSvMV9gSuuwdmo069QpDhx6ww87QbmedLBCTvAe/mRUCtwPHA4uBV81sqru/ke9aEuMOXhWGqsroeeWXz6s2hqGyIgxVFeGqycry8LhxA1R8Htrfy9eGvfbyshDwG1aHftU//xTWlUJZKWxcv/n6W7SBjj1D+2u/86Brb9hpv3DQTkEvDa2oJZQcGQYIf+fLF8Ky12HZAlj+Bnw8B16fHP4PMrVuD9sXh6FN5/C6dYfQZNSyLbRqGx6LWkOL7cJjUavwgVLUCgqKwjfVghbheUFhGKwQrCB6XpAxpOPvP4k9/oOBd9z9PQAzewgYDDR88D91FcwZU/d87jksLGOezebPNt6j51keY2PRP0X7cIZNm87ha3SbLuHK2U17UB1LoN1OqfkDl0aooDDch2GnPsDZX47fWA6rPwrDmiWh64+yZWEnpqw0fFPdsCrs3JTH2XmcRf8f1R+p9jx6vdlba5mWdVU5zHP2/eEbeANKIvh3AT7KeL0YOKT6TGY2EhgZvSwzs7fyUFtD6wJ8mr/Vrc7fquonz9ulyahzu9iv81RJ46G/lZ8NzDY21+2yW7aRSQR/to+4LXaF3X00MDr+cuJjZrPcvX/SdTQ22i7ZabtsSdsku/pulyT66lkMZF7i1x1YkkAdIiKplETwvwrsaWY9zawlcA4wNYE6RERSKe9NPe6+0cwuA/5GOJ3zXnd/Pd915EmTbqqKkbZLdtouW9I2ya5e28U8pzNaRESkuVB//CIiKaPgFxFJGQV/PZnZSWb2lpm9Y2ajskwfYGarzWxuNPwiiTrzra7tEs0zINomr5vZ8/muMQk5/L38KONvZYGZVZpZpyRqzacctkt7M3vMzOZFfy8XJVFnvuWwXTqa2SQzm29mr5hZn5wW7O4atnEgHJx+F+gFtATmAb2rzTMAeDzpWhvhdulAuFq7R/R6x6Trbgzbpdr8pwLPJF13Y9guwFXAr6PnxcAKoGXStTeC7fK/wDXR868AM3JZtvb46+e/3U+4ezmwqfuJtMtluwwDHnX3DwHcfXmea0zC1v69nAuMz0tlycpluzjQzswMaEsI/o35LTPvctkuvYEZAO7+JlBiZl3rWrCCv36ydT+xS5b5Dou+oj5pZvvmp7RE5bJd9gI6mtlzZjbbzC7IW3XJyfXvBTNrA5wETMxDXUnLZbv8EdiHcLHna8AV7l6Vn/ISk8t2mQecAWBmBxO6aOhe14LVEXb95NL9xBxgN3cvM7OTgcnAnnEXlrBctksRcCAwENgOmGlmL7v7f+IuLkE5dVcSORV4yd1XxFhPY5HLdjkRmAscC+wOTDezf7j7mphrS1Iu2+Vm4PdmNpfwgfhvcvgmpD3++qmz+wl3X+PuZdHzJ4AWZtYlfyUmIpduORYDT7n7Onf/FHgB6Jun+pKyNd2VnEM6mnkgt+1yEaFp0N39HeB9Qpt2c5Zrvlzk7v2ACwjHP96va8EK/vqps/sJM9spapfc9FWsAPgs75XmVy7dckwBvmZmRVGzxiHAwjzXmW85dVdiZu2BownbKA1y2S4fEr4dErVh7w28l9cq8y+XfOkQTQP4NvBCLt+C1NRTD15D9xNmdkk0/Q7gLOC7ZrYRWA+c49Eh+OYql+3i7gvN7ClgPlBFuBPbguSqjl+Ofy8AQ4C/u/u6hErNqxy3y/XAfWb2GqEJ5CfRN8VmK8ftsg8w1swqCWfJjchl2eqyQUQkZdTUIyKSMgp+EZGUUfCLiKSMgl9EJGUU/CIiKaPgFxFJGQW/iEjKKPhFtoGZHRT1gd7azLaP+ojPrS90kYTpAi6RbWRmNwCtCZ3MLXb3XyVckkhOFPwi2yjqI+VVYANwuLtXJlySSE7U1COy7ToRbgrSjrDnL9IkaI9fZBuZ2VTCXZF6At3c/bKESxLJiXrnFNkG0R3DNrr7ODMrBP5pZse6+zNJ1yZSF+3xi4ikjNr4RURSRsEvIpIyCn4RkZRR8IuIpIyCX0QkZRT8IiIpo+AXEUmZ/wPV6OBjv05UcgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ns = np.array([10, 100, 1000]) # Зададим значения, которые будем учитывать как размер выборки\n",
    "a = -wind\n",
    "b = wind\n",
    "N = 100\n",
    "delta_x = (b-a) / (N-1)\n",
    "x = np.linspace(a, b, N)\n",
    "for n in ns:\n",
    "        \n",
    "    summa = []\n",
    "\n",
    "    for r in np.arange(1000):\n",
    "        \n",
    "        sample_sum = np.sum(x[np.random.randint(len(x), size = n)])/n\n",
    "        summa.append(sample_sum)\n",
    "\n",
    "\n",
    "    plt.hist(summa, density=True)\n",
    "    plt.title(f'Convolute Distribution ({n})')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('pdf')  \n",
    "\n",
    "    sigma = sigma_gen/np.sqrt(n)\n",
    "    mu = mu_gen\n",
    "    print(f'Средене значение выборки n = {n}: {np.mean(summa)}')\n",
    "    print(f'Средене значение N(sigma, mu) n = {n}: {sigma}')\n",
    "    print(f'Cреднеквадратическое отклонение выборки n = {n}: {np.std(summa)}')\n",
    "    print(f'Cреднеквадратическое отклонение N(sigma, mu) n = {n}: {mu}')\n",
    "    norm_rv = sts.norm(loc=mu, scale=sigma)\n",
    "    x = np.linspace(mu-5*sigma, mu+5*sigma, 100)\n",
    "    pdf = norm_rv.pdf(x)\n",
    "    plt.plot(x, pdf)\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "c9f45c5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1, 2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "de612939",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "dfc24561",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "f3115d4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.816496580927726"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(2/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "727e601b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6666666666666665"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "8/3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f4abaa69",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aa65939c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}