VS-CDR/probability-theory.ipynb

## probability-theory.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "language": "python",
      "display_name": "Python 3 (ipykernel)"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/VS-CDR/b2c46e433cd845852e38b003e69c7d6a/probability-theory.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZJbJBdDwYvaY",
        "ExecuteTime": {
          "end_time": "2023-11-15T21:35:07.571948250Z",
          "start_time": "2023-11-15T21:35:07.096679131Z"
        }
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from enum import Enum\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "rng = np.random.default_rng()"
      ],
      "metadata": {
        "id": "7xj2picyZFcP",
        "ExecuteTime": {
          "end_time": "2023-11-15T21:35:07.574015291Z",
          "start_time": "2023-11-15T21:35:07.572278739Z"
        }
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "30. Сгенерировать результат следующего эксперимента: 100 раз подбросили\n",
        "симметричную монету. Предполагаем, что выпасть может или орёл (исход \"1\"), или решка (исход \"0\"). Посчитайте долю выпадений орла."
      ],
      "metadata": {
        "id": "s_PFb3PdZvZw"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [],
      "source": [
        "Result = Enum('Event', ['eagle', 'tail'])"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-11-15T21:41:55.181449309Z",
          "start_time": "2023-11-15T21:41:55.140059822Z"
        },
        "id": "5OJYIkzgL8Iu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def experiment_with_a_coin():\n",
        "  events = [Result.eagle, Result.tail]\n",
        "  probabilities = [0.5, 0.5]\n",
        "\n",
        "  number_of_throws = 100\n",
        "  experiments = rng.choice(a=events, size=number_of_throws, p=probabilities)\n",
        "\n",
        "  eagle_event_cnt = 0\n",
        "  for result in experiments:\n",
        "    if result == Result.eagle:\n",
        "      eagle_event_cnt += 1\n",
        "\n",
        "  return eagle_event_cnt / number_of_throws"
      ],
      "metadata": {
        "id": "2IbueYrRY3BF",
        "ExecuteTime": {
          "end_time": "2023-11-15T21:41:55.453883420Z",
          "start_time": "2023-11-15T21:41:55.450260782Z"
        }
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f'Доля выпадения орла : {experiment_with_a_coin()}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KZ352O7C3RA4",
        "outputId": "138188c0-e2a2-4a11-838a-8d80f22185a9",
        "ExecuteTime": {
          "end_time": "2023-11-15T21:41:57.154690122Z",
          "start_time": "2023-11-15T21:41:57.151910315Z"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Доля выпадения орла : 0.49\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "num_of_results = 1000000\n",
        "n_bins = 100\n",
        "\n",
        "results = [experiment_with_a_coin() for i in range(num_of_results)]\n",
        "\n",
        "fig, axs = plt.subplots(tight_layout=True)\n",
        "\n",
        "axs.hist(results, n_bins)\n",
        "\n",
        "axs.set_xlabel('Доля')\n",
        "axs.set_ylabel('Количество')\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "0JbldsRtZbaq",
        "outputId": "a28623da-1b71-478b-a965-59ab519a9280",
        "ExecuteTime": {
          "end_time": "2023-11-15T21:37:43.749048382Z",
          "start_time": "2023-11-15T21:36:13.677216435Z"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "31. Метод Монте-Карло для приближенного вычисления площади фигуры.\n",
        "\n",
        "Пусть М1 = {$(x,y) \\in \\mathbb{R}^2: 0 ≤ x ≤ 1, 0≤ у ≤ x^2$}.\n",
        "\n",
        "Чему равна вероятность того, что точка, выбираемая случайным образом из множества Q = {$(x,y) \\in \\mathbb{R}^2: 0 ≤ x ≤ 1, 0≤ у ≤ 1$}, попадет в М?\n",
        "\n",
        "Провести следующий численный эксперимент.\n",
        "\n",
        "Смоделировать выборку размера и из равномерного распределения на множестве и найти долю элементов выборки, попавших в М1. В качестве нужно использовать следующие значения: 10, 100, 1000.\n",
        "\n",
        "С помощью аналогичных рассуждений найти (приближенно) площадь множества\n",
        "\n",
        "М2 = {$(x,y) \\in \\mathbb{R}^2: 0 ≤ x ≤ 1, 0≤ у ≤ cos(sin(x))$}"
      ],
      "metadata": {
        "id": "YPBCt7sScuwj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![photo_2023-11-05_19-57-37.jpg](data:image/jpeg;base64,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)\n",
        "\n",
        "![photo_2023-11-11_13-32-43.jpg](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAQDAwQDAwQEAwQFBAQFBgoHBgYGBg0JCggKDw0QEA8NDw4RExgUERIXEg4PFRwVFxkZGxsbEBQdHx0aHxgaGxr/2wBDAQQFBQYFBgwHBwwaEQ8RGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhr/wgARCACdANoDASIAAhEBAxEB/8QAGwABAAIDAQEAAAAAAAAAAAAAAAQFAQIGAwf/xAAYAQEAAwEAAAAAAAAAAAAAAAAAAQIDBP/aAAwDAQACEAMQAAAB+nwe41tWo3g2e8eW26XvPoYlXVOY9KujUU+kzhSwAAAAAABTeBFs6yz66hYAAiyiK33lka29RX5z1LnJOS6a7Z3AAAAo8Xo5WzrLPqqFwAAAADXYVvtMK63FNAznqXOSsly12zuBH25jU9bOss+qoXAAAAAAAANdhS2fld5RW72+mU7iluVs6yz66hYAAAAAAAABDu6S7wmQMZ5yLdzDm7Oss+qoXAAAAAAAAAQ7uku8JkDGSrwVVnWWfXULAAAAAAAAAId3SXeEyBjPPel6OVs6yz6qhcAAAAAAAABDu6S7wmQMZIQorOLJ6IywmMtcmTBljBswMsYNjBlgZa5MsCJd1M/KZ6FtnMvmOngFdcxLEzX2HmVflN1LIHMaXfse24edB0daVfTQJ45/oIBV2eZR64yKivvvEng//8QAJRAAAgIBAwQCAwEAAAAAAAAAAwQBAgAQEzMFETRAFDASFSAi/9oACAEBAAEFAkXb0lR0vyK9Ui8/ss/Z0z9qrlHliZE9/V2h5UAqEW5tbAFfPgAzZNTIO6PI6l+OBcAf01ub6CriNkLWFkMuCynU15mJiY+xN2zFlup/IcW5vrmsWj4VKzBnA5TqYe8TFo+lZEi8g6fITq8/3TEWj4dKTB3A5TqYLT37/StzejasXj4dR5DDgcp1MEzExaNRnEbILSSLc3qTEWg6tAiHD1B/P28/aJ50/wDzfp9ThbW5/Vb8UPDn4xqtzeq34oeH+Fub1W/FDw6IGNJFuq1Z6otz+q34oeHQKAAZtVkq3N6rfih4f4W5vVb8UPDoq9RqRPVIdbm9VvxQ8OiirAbAE18tbn9VvxQ8P8Lc3qt+KHh/hbm9VvxQ8OkSx2iWMEqcZNpjvtMd9pjJCeckTHbaPkCY7QJjICfNpjvtMZImMsE8xtHyBMdoExm0xmyfvtMd9pjJExhljlDTfpSJY7fkfRtg1DPFNuhvuCx41gKK2LBErGk2jbBqG611L4Qa2i9cvb8KIGNJEnbmY0eKbdcZNsIlsdPRG5bSqwax9SpBMUyIDxpelS0EmEMLIhT1KkExbAoQOoUAAyiYRm0YTC1hUxGgY6hHpsUiRpBEbT//xAAbEQACAwEBAQAAAAAAAAAAAAAAARESITBRYP/aAAgBAwEBPwGGaaSyxZd48NLLvHhLLLvVG/K//8QAIhEAAgEEAQUBAQAAAAAAAAAAAQIAAxIwMRAREyAhUUBB/9oACAECAQE/Aeo+RVUiWJO0s7R/kKMMS68T0O4aanUNNh5rrAfe4aanUNNh4LrHUb3Oq/OF1jqcrrHU5XWOpyusdTlXAEvWXrL1l6y9ZesvWXrL1l6xyDr8H//EAD8QAAECAwIHDgUDBAMAAAAAAAECAwAREgQhEBMiMUFz4SAyQFFhcXJ0gpGSscLRIzBCYqEkM8E0gYPwFGOT/9oACAEBAAY/ArUktWt+TtxUm8ZKYbVRaVqcLtaahK46BO6ULAstomhVJuTn74/pbT4R7xlM2hP+KMpwo6SCIyH2z2ou4KchN6qjdp4/xCnENoS4rfKCbzFt6x6RuMttCudMTQjFn7FFMfCtbo6clxeGXx/dBj9RZ3WuWVQ/EfCdQo8U7+B23rHpHyfitpVziP01oda5Cah+Y+I0h8caDSe6JOksK4nRTEwZj5tLrWKqbDiMqc0+8Ls+LApqzLmoSMsoaJ6ItvWPSPmSUJiJ2dS7Of8ArP8AEX0WlPgV7RS9VZ1cTgl+YmkzHygVPhwpQltPw/pH988BZdCkIroFEjlG+Z0xbtf6R8+ShMROzqXZz9hu7oykotKeTJV7RS4SwvicEou+TbesekcCkoBQ5YnZlrs5+w3d0ZaUWlP25Kok7UwricEomkzG4ViXEOUmSqVTlBbC0lwCZTO+Lb1j0jgslCYh1yzFTCwkn4Zl+ISoLbtAInJQpMfqrO6zyyqHeI/qG++GziXGgizoaVNsjKn/ALfCkHGEKW4p2puSc+SQrTFu1/pHBn9WryhvojBmGG29Y9I4M/q1eUN9Ebm29Y9I4M/q1eUN9EYUJfdxuMYDu9ApPFzRi27Q0WShQSgKEyoEX+fdFu1/pHBn9WryhvojCcUkpzfWdGYc3JAdllhJSDyf6ItvWPSODP6tXlDfRG5tvWPSODP6tXlDfRGGQQ43khaaxvknTGKxbiJzoUoXKlni29Y9I4M/q1eUN9EYUqdxRKG0tJpUbxpOb8Qty0oZIMwlQdOSnilT/MW7X+kcGf1avKG+iNzbesekcGf1avKG+iNzbesekcGf1avKG+iMImhsnWbIvQ2f8myH1SbONcr35uuHJyRmb8eyMzfj2QLm/HsjM2O2faLg2O3sjet+M+0Xhs9vZF4bPb2Qbm7/ALz7Rmb8eyBc349kXBsdvZBEmx2z7RvW/GfaLw2e3si8Nnt7INzfj2ROTfjPtGZvx7IFzfj2RcGx29kONybFSSJ1n2hKaG7hL9w+0CaGydZsj9tv/wBD7YHlNuUIYCDRSMuZvihh3E0sqcnSDMjnhteapIOB5xvfJTdFoZccxxblSpQAzjkh1Lj3/IbSAKqQMvSByYXlNuUIYCDRSMuZvgoaebafKCoFRGYQFIIUkiYI04FKzyE4Ql93G4xgO70Ck8XNCsdjEpWpaWhSKck988NDDuJpZU5OkGZHPFlLFYW8bw2BVKmd1V0MuOEFak5UuPDakPuYwtu0g0y+lJ/mGVLcqQ+XBRSMmRu3AdcRNYl9RvlmnxwA6kqlP6zpzjm5MKkOCpKhIiJNhQvmcskm6UfAxgEpSU6pQ7icIdcRNYl9RvlmnxwtpYKm1zmCo6dwcUkpzfWdGYc3JBeQiSzPSZX57sIx6apXXKIu4roksK31QksiRlK7ihKGxShIkBhWQCK1hapKN5u9hBdQiSzP6jpz3aMP/8QAKBABAAEDAgUEAwEBAAAAAAAAAREAITFBURBAYaHwIHGRsTCB8cHR/9oACAEBAAE/IRLUZUE0MpF1Y60qP+dIWZI4DTOtdM8SQH7lMM/M0j7sn6o1y8qSsk+0Z+KAShNzlVrnisbmI9xC/QrGtFD3XWu/eh7Tg1GyNz6Bo+P0DuT3rBc2UfZQ/uQ77/irPtp9GeT79+F+XO581+mjtOniHRdbvQpl/tY70KEmEfyhwuBXzexGFr5zX/AGJj1rmSu/fkWQGyJNSzD0R+lYr5jxFLEp2T/HejAEwjP4mqWLCGvOpGtjpT3AQ6gufofugTATOfzrgCZEmphx6a98K/eW+tl2oqqf3cPzQAKEcJ+Hv3JK15yCShnRz7e1fuGLtNvqhjr/AK+O9GAJhGfQ6FLRSbMYqHaImBuld+5VcAbIk0bTawlDXCgF5XdZbtU/2I+c9qEqTjdlIaBa4X2XzUOowITOAuSLSwbRU+hPlnxG6vNbcJ8/Fx79yz4jdXmtvT37lnxG6vNbcYsG9SBuIN1pltmpHAyLyNb4m0vZ2Nnpyz4jdXmtuOTd7UUhe3Qt0pUssGpFOyu/cs+I3V5rb09+5Z8RurzW3FGsYgNAIX4YelBrNYpLiF511Ca79yz4jdXmtuOheNBbuhjF3vRJqSR0REXtL/gKNzd68s+I3V5rb09+5Z8RurzW3p79yz4jdXmtuJiOF2V6iLtLqquhQDYEUXjbjEq2jbjEqrMDhvdepUF4P7qKQtFmVuE6IC0XZXqI1Z1VCtaUmlal424xKqzA4b3Xqo1Y1VDjEicXAdEBaLsr1Eas6qhMnltdapLskCKlo24xKqzA4b3Xqo1Y1V1MGREkTS8HFKiYjhdlfjEvLucCVcpOC0RfeiSsvEiADDGZi/UpXSUTtJwgamrSQdGnmqapkhgGfumkoDCXWhcWzMNpzxeXc4Eq5ScFoi+9YRHJNgcq2D3dKP8AmWkDhHhaa7hvUWDepA3EG60y2zR+VZCxDPSm8G2OJJWXiRABhjMxfqUyNTKXIvcRnTrQCUqEdVuJ0o8AxaR7qlx20hpiE4LzOdPQmrNQEkwDEG5M1hV2wsKUZut1sUAABAcDKrKwjkq6xNlxqKy23xbarRGwFx0QHFNWagJJgGINyZo4wBhJleZ19GTd7UUhe3Qt0q/4TMHISgXWC/G92FGRZUiRgs2rcrBPWAzZodd6OPALQ4jhLAEIDXa1im3ZaQJTBMScxnj/AP/aAAwDAQACAAMAAAAQDJAqHBAAAAAAAAMpAAAThQHIAAAAQLAAAAAAABoLAAIjAAAAAAAAAAFwApAAAAAAAAAAUAwLAAAAAAAAAAUAEpAAAAAAAAAAUAwLAAAAAAAAAAUAAgDLLHDHLDLDbAQcAcAwAQAEIQQA/8QAIhEAAgEDBAMBAQAAAAAAAAAAAAEREDAxICFBYVFxoUDh/9oACAEDAQE/EOwa8j3+f0h4R2QmbTaedDSezIrKCV7Fyba3mxFeBD2Lk296Hm2uDYhcP5R5tqrzbVXm2qvNtVaIZDIZDIZDIZDIZDF+D//EACYRAAECBAUEAwAAAAAAAAAAAAEAMREwYfAQICFxoUBBUZGB0eH/2gAIAQIBAT8QSCCQo3Y+/wARIxIv4R7wFaiRKbyAkahAyjfl06Ic3ymQR2uOduRA3G/Lp0Q5vlMwjtkblkAR13UV/Q/YODct4xblvGLct4xblvGIICVWVZVlWVZVlWVZVlWR0dA//8QAJxABAQABAgUEAwEBAQAAAAAAAREhADEQQVFxgUBhkfAgMKGxweH/2gAIAQEAAT8QJtNBQyR2QAhhnSjMFnEahKwqrSOmd0G4RB4aujXU/wAWptM5oR/eh45wI/kT+6ZB5sf9y6DueyUfSotinTerGcSsmLY0FP4V3tl8n8et3I7/APZNL6vkcD4jWc9ptCPoJRX/AJaw0vZx96r8jSZ0ZoO7g+PWdQI70KO248azgByF+eeE1iSnMz6tU9hrEdwRXZ5+NCTLRkT2T9u7JNWU6S3CMIs6zcmVCRqGKpzDGj+zXFXoYPcdWyKqrvd1njWHHczJ/q0p7kKZ9smaAU+jBOon6tyaBjoBsYmCDziSt7wu9WB2nIWgdDrE0GWRH5/v7xqdBgnuOrLtVtPdr+NYMjzvMq+B0xD0H32f8louzVFE7+r67UIFTuOkLm3cH3o/g1ghntLq0fh0x/UHF7ZvxoPT6ME9k/CWvB3fDWNnQUrKD9qaD1T03UelQYPcdJcNC4pzJTpptdI8wMLvujW3m8k/lfkaCGVLGX4dBmgVmFDm6RSXhZGCnAIHKwOjJI0alHHJkcub29PQ+16OC5Vq1U59V1ofa9H4zjly+n6H2vRxXmXoMCGqjYKquIbIq52DEPUtndDcyrcpnm7O3p6H2vRxHy3kO1gXNXYlRhTV6dSsRRZlWy4931HWh9r0es60PtejjnDkH5NmMcgpRTSrjomDBRiExGSnqOtD7Xo4lCekBLdkgQikZaJtWn+rYFCzFDkAzMo3KY5Oxv6eh9r0fjOM6uPT9D7Xo9Z1ofa9HEECCLUyzZpkWAMYKodhDxpouZLL3vzXG+2NAMZgNu5reqnxpQhFDv3Eb0R+dMBlBeI46Mo+NF1xYbAFO8J50zsor1yZu4ICdkEeubNmkApSzwrDsIeNBx4jgQQ7xfOgGMwG3c1vVT40wGUF4jjoyj40AFKW+BKdxTzpLewaJN+FATsgj1zZs0gFKWeFYdhDxpgMoJxDHVkXzoLnCYgi176fGlCEUO/cRvRH50wGUF4jjoyj40AFKW+BKdxTzokPNORsE2WymhyvUFgFnZoECCLUyzZxatZFFIIMAgVil5NJTKZNCxM1gVJzLMxOsDP7wh5xohiHMFqe2kMiOJjLEC0BgMpU4M6wuLoM8iNEBwayKKQQYBArFLyaILB2QbY86R3yYIadBmqBhERE34OTYr2BZ/NLzL0GBDVRsFVXCmqCk2FUxrrAOTwSmUyaFiZrAqTmLWkvYElMFM4IZAvCbKWIKCIiJDI8GxmHldAyifTlBcEVVnN0EcEwbCIbUrTRyfhKwAAZSEBEDCqTQ8tUORAKgKjIJAA0QIAQDgcrq6NEOiOlF6KzyOxxBJCIhDDcD01mxDcB+eMrAABlIQEQMKpNPERwMU3AygJCBADigiJR3ND5byHawLmrsSowppYCaLEFNOlQK3XjVvLEGNm4RZQozVNgAOTIeG1UG0ZUp+tjDY/94voIwpBmyB3AaNbSUlScGYYhRKy3j//Z)"
      ],
      "metadata": {
        "id": "-nP0ib8zbDhX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.integrate import quad\n",
        "\n",
        "M1 = quad(lambda x: x**2, 0, 1)\n",
        "M2 = quad(lambda x: np.cos(np.sin(x)), 0, 1)\n",
        "\n",
        "print(f'Площадь множетсва M1 = {M1[0]}, Площадь множества = {M2[0]}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "82qAWacK5WTi",
        "outputId": "bb6a7834-8adf-4909-f7bb-e3bf2b028a66"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Площадь множетсва M1 = 0.33333333333333337, Площадь множества = 0.868740039576976\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def is_in_M1(x, y):\n",
        "     return (0 <= x <= 1) and (0 <= y <= x**2)\n",
        "\n",
        "def is_in_M2(x, y):\n",
        "     return (0 <= x <= 1) and (0 <= y <= np.cos(np.sin(x)))"
      ],
      "metadata": {
        "id": "_kpPfL7F8fFm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "set_limitations = {\"M1\" : is_in_M1, \"M2\" : is_in_M2}"
      ],
      "metadata": {
        "id": "lL7ZlJgp8Ojj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def method_Munte_Carlu(set_lims, set, extra=False):\n",
        "  dim = 2\n",
        "  sample_size = [10, 100, 1000]\n",
        "\n",
        "  if extra:\n",
        "    sample_size.append(10000)\n",
        "\n",
        "  for size in sample_size:\n",
        "    sample = rng.uniform(size=(dim, size))\n",
        "\n",
        "    cnt_inside = 0\n",
        "    for i in range(size):\n",
        "      x, y = sample[0][i], sample[1][i]\n",
        "\n",
        "      if set_lims[set](x,y):\n",
        "        cnt_inside += 1\n",
        "\n",
        "    proportion_of_inside = cnt_inside / size\n",
        "    print(f'Доля точек, попавших в M_1 = {proportion_of_inside}')\n"
      ],
      "metadata": {
        "id": "UOkT07U9Zbz4"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "method_Munte_Carlu(set_limitations, 'M1')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8WMg0c-268jT",
        "outputId": "fbfc874e-50fa-41eb-a482-d09e6ccc7405"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Доля точек, попавших в M_1 = 0.3\n",
            "Доля точек, попавших в M_1 = 0.33\n",
            "Доля точек, попавших в M_1 = 0.309\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Заметим, что с увеличением числа точек доля, попавших M_1 все лучше приближает реальную площадь."
      ],
      "metadata": {
        "id": "U99tOY0i69pr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "method_Munte_Carlu(set_limitations, 'M2')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-DDWBHOH7Vhg",
        "outputId": "29a84a5e-42d2-4984-f497-dc9341e79ae4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Доля точек, попавших в M_1 = 0.9\n",
            "Доля точек, попавших в M_1 = 0.87\n",
            "Доля точек, попавших в M_1 = 0.892\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "method_Munte_Carlu(set_limitations, 'M2', True)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "H37Xjoej9IRK",
        "outputId": "853be97b-1bbe-4679-f86c-79984921b1d4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Доля точек, попавших в M_1 = 0.9\n",
            "Доля точек, попавших в M_1 = 0.86\n",
            "Доля точек, попавших в M_1 = 0.881\n",
            "Доля точек, попавших в M_1 = 0.8775\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "32. Задача вычислении с помощью «иглы Бюффона».\n",
        "\n",
        "Бросим случайным образом иглу длины 1 на горизонтальный лист бумаги, разлинованный параллельными прямыми так, что расстояние между соседними прямыми также равно 1. Чему равна вероятность того, что упавшая игла пересечет линии бумаги. Повторим этот опыт N раз. Смоделировать, как будет расти с ростом N (т.е. при $N → ∞$) число пересечений упавшей иглы с линиями бумаги. Как полученные в эксперименте значения позволяют вычислить $\\pi$? Оценить погрешность вычислений с помощью центральной предельной теоремы."
      ],
      "metadata": {
        "id": "tLLpZDqW-V4P"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from math import ceil\n",
        "from tqdm import trange"
      ],
      "metadata": {
        "id": "BUReEBxme4Jw",
        "ExecuteTime": {
          "end_time": "2023-11-15T22:29:53.481278891Z",
          "start_time": "2023-11-15T22:29:53.435307381Z"
        }
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "![Снимок.PNG](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "zagmKaj_BHjN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Рассмотрим произвольную иглу в xOy:\n",
        "\n",
        "заметим что достаточно рассматривать такие иглы, которые образуют угол $ 0 ≤ φ ≤ \\pi$ с положительным направлением Ox(другие иглы получаются из этих лишь обменом конца и начала).\n",
        "\n",
        "Отсюда получаем критерий пересечения прямой и иглы:\n",
        "\n",
        "Если расстояние от нижнего конца иглы до ближайшей прямой сверху (dist) < разности по Оу координат концов иглы, то есть пересечение"
      ],
      "metadata": {
        "id": "xD81jJ7m9he2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$diff_y = len(match) * sin(φ) \\implies len(match) * sin(φ) > dist$"
      ],
      "metadata": {
        "id": "IdxXny_EDgVC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Откуда вероятность попадания $ P = \\frac{\\int_{0}^{\\pi} len(match) * sin(φ) \\,dφ}{\\pi * width} = \\frac{2 * len(match)}{\\pi * width} = \\frac{\\text{кол-во пересечений}}{\\text{кол-во бросков}}$"
      ],
      "metadata": {
        "id": "7B8QZq7IEeOc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "borders = [\n",
        "    [0, 10],\n",
        "    [0, 10],\n",
        "]\n",
        "\n",
        "def drop_matches(up_lim, width=1, match_len=1):\n",
        "  cnt_intercepts = 0\n",
        "  cnt_misses = 0\n",
        "\n",
        "  for i in trange(up_lim):\n",
        "    y_beg = borders[1][0] + (borders[1][1] - borders[1][0]) * rng.random()\n",
        "    y_end = y_beg + match_len * np.sin(np.radians(180.0 * rng.random()))\n",
        "\n",
        "    closest_y = ceil(y_beg)\n",
        "\n",
        "    y_diff_beg = closest_y - y_beg\n",
        "    y_diff_end = y_end - y_beg\n",
        "\n",
        "    if y_diff_end > y_diff_beg:\n",
        "      cnt_intercepts += 1\n",
        "    else:\n",
        "      cnt_misses += 1\n",
        "\n",
        "    if i % (up_lim / 10) == 0 and cnt_intercepts > 0:\n",
        "      calc_proba = cnt_intercepts / (cnt_intercepts + cnt_misses)\n",
        "      est_pi = (2.0 * match_len) / (calc_proba * width)\n",
        "      print(f\"\\n Количество пересечений: {calc_proba}\")\n",
        "      print(f\"\\n Рассчитанное значение числа Пи: {est_pi}\")\n",
        "\n",
        "  calc_proba_final = cnt_intercepts / (cnt_intercepts + cnt_misses)\n",
        "  return (2.0 * match_len) / (calc_proba_final * width)\n"
      ],
      "metadata": {
        "id": "Zfmn_9DA68J0",
        "ExecuteTime": {
          "end_time": "2023-11-15T22:30:36.781330172Z",
          "start_time": "2023-11-15T22:30:36.740433555Z"
        }
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Если $X_{i}$ независимы и одинаково распределены, $Z_{n}=\\frac{\\bar{X}_{n}-\\mu}{\\sqrt{\\frac{\\sigma^{2}}{n}}}$,\n",
        "$Z\\sim N(0;1)$, то:\n",
        "\n",
        "\\begin{equation}\n",
        "|\\mathbb{P}(Z_{n}\\leq t)-\\mathbb{P}(Z\\leq t)|\\leq c\\cdot\\frac{\\mathbb{E}(|X_{i}-\\mu|^{3})}{\\sigma^{3}\\sqrt{n}}\n",
        "\\end{equation}\n",
        "\n",
        "Возьмем $c = 0,5$.\n",
        "\n",
        "Применим эту теорему к биномиальному распределению:\n",
        "\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        "В этом случае:$\\mathbb{E}(X_{i})=p$, $\\mathbb{Var}(X_{i})=p(1-p)$, $\\sigma=\\sqrt{p(1-p)}$ и $\\mathbb{E}(|X_{i}-p|^{3})=p(1-p)(p^{2}+(1-p)^{2})$:\n",
        "\n",
        "\\begin{equation}\n",
        "\\frac{\\mathbb{E}(|X_{i}-p|^{3})}{\\sigma^{3}\\sqrt{n}}=\\frac{p(1-p)(p^{2}+(1-p)^{2})}{(p(1-p))^{3/2}\\sqrt{n}}=\\frac{p^{2}+(1-p)^{2}}{\\sqrt{p(1-p)n}}\n",
        "\\end{equation}"
      ],
      "metadata": {
        "collapsed": false,
        "id": "ok2nhezRL8Iz"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.017433720114437952\n"
          ]
        }
      ],
      "source": [
        "from math import sqrt, pi\n",
        "\n",
        "p = 2 / pi\n",
        "var = p * (1 - p)\n",
        "n = 100000\n",
        "\n",
        "sigma = sqrt(var)\n",
        "\n",
        "diff = (((p**2 + (1 - p)**2) / sqrt(var * n)) / (2 / pi)) * pi\n",
        "print(diff)"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-11-15T22:30:38.151399455Z",
          "start_time": "2023-11-15T22:30:38.110924486Z"
        },
        "id": "h84CaqBqL8Iz",
        "outputId": "2d2c76d5-e74e-43cf-c7f5-77dd2dd78b08",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "assert abs(drop_matches(n) - pi) < diff"
      ],
      "metadata": {
        "id": "zbd73JEDeQPC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8fd9a45c-8004-4625-8a94-79f3c4caa78b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            " 14%|█▍        | 14204/100000 [00:00<00:00, 142018.13it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Количество пересечений: 0.628937106289371\n",
            "\n",
            " Рассчитанное значение числа Пи: 3.1799682034976153\n",
            "\n",
            " Количество пересечений: 0.6362681865906704\n",
            "\n",
            " Рассчитанное значение числа Пи: 3.1433286185761435\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r 28%|██▊       | 28406/100000 [00:00<00:00, 130212.01it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Количество пересечений: 0.6358788040398653\n",
            "\n",
            " Рассчитанное значение числа Пи: 3.145253446558683\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r 41%|████▏     | 41493/100000 [00:00<00:00, 118401.23it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Количество пересечений: 0.6352341191470213\n",
            "\n",
            " Рассчитанное значение числа Пи: 3.1484454939000392\n",
            "\n",
            " Количество пересечений: 0.635907281854363\n",
            "\n",
            " Рассчитанное значение числа Пи: 3.1451125927789656\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r 56%|█████▌    | 55649/100000 [00:00<00:00, 126747.41it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Количество пересечений: 0.6360060665655572\n",
            "\n",
            " Рассчитанное значение числа Пи: 3.1446240926600457\n",
            "\n",
            " Количество пересечений: 0.6363766231910972\n",
            "\n",
            " Рассчитанное значение числа Пи: 3.1427930051406383\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 100000/100000 [00:00<00:00, 151068.68it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Количество пересечений: 0.63699203759953\n",
            "\n",
            " Рассчитанное значение числа Пи: 3.1397566718995287\n",
            "\n",
            " Количество пересечений: 0.6366929256341596\n",
            "\n",
            " Рассчитанное значение числа Пи: 3.1412316981658903\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "33. Сгенерировать 100 значений из биномиального распределения"
      ],
      "metadata": {
        "id": "4IqUOPdt_4nn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "size = 100\n",
        "\n",
        "x = [i for i in range(1, 100 + 1, 1)]"
      ],
      "metadata": {
        "id": "04F__S4RASQi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "n, p = 100, 0.01\n",
        "a = rng.binomial(n, p, size)\n",
        "\n",
        "n, p = 200, 0.005\n",
        "b = rng.binomial(n, p, size)\n",
        "\n",
        "n, p = 400, 0.0025\n",
        "c = rng.binomial(n, p, size)\n",
        "\n",
        "poisson_1 = rng.poisson(lam=1, size=size)"
      ],
      "metadata": {
        "id": "g3sPWMO5_Idf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import seaborn as sns\n",
        "import pandas as pd\n",
        "\n",
        "BinA = pd.DataFrame({\"Bin(100, 0.01)\" : a})a\n",
        "BinB = pd.DataFrame({\"Bin(200, 0.005)\" : b})\n",
        "BinC = pd.DataFrame({\"Bin(400, 0.0025)\" : c})\n",
        "\n",
        "Bin = pd.concat([BinA, BinB, BinC])"
      ],
      "metadata": {
        "id": "8hn24rsTn2r1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "sns.histplot(\n",
        "    data=Bin,\n",
        "    element=\"step\",\n",
        "    discrete=True,\n",
        ")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "gFo6AKczn55x",
        "outputId": "65219256-e5c3-45b4-b2f8-2c564eaae657"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: ylabel='Count'>"
            ]
          },
          "metadata": {},
          "execution_count": 29
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sns.histplot(\n",
        "    data=pd.DataFrame({\"Poisson_1\" : poisson_1}),\n",
        "    discrete=True,\n",
        "    element=\"step\",\n",
        ")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "Dndff6XGqhuJ",
        "outputId": "abdbdf6f-432d-48b7-bce0-67dfe83be17b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: ylabel='Count'>"
            ]
          },
          "metadata": {},
          "execution_count": 30
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjIAAAGdCAYAAAAIbpn/AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAn3ElEQVR4nO3de3RU9b3//9cQkkmAZGK45CITCHIHgy1QmmI5XMIlVAolx3o7JbgUhROoIdXaeJSLx/7iqr8itsRAz7FAT02xdgkqi0IlknBsgUI4kYuSRTixhEsSRHKFTGJmvn/4Zb5GCIYQsvcnPB9rzVrM3nv2vBlc8mTvPTsOn8/nEwAAgIG6WD0AAABAWxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIzV1eoBbjav16szZ84oNDRUDofD6nEAAEAr+Hw+1dTUKCYmRl26tHzcpdOHzJkzZ+R2u60eAwAAtEFpaan69u3b4vpOHzKhoaGSvvggwsLCLJ4GAAC0RnV1tdxut//v8ZZ0+pC5fDopLCyMkAEAwDBfd1kIF/sCAABjETIAAMBYhAwAADBWp79GBgDQefh8Pn3++edqamqyehTcoICAAHXt2vWGb41CyAAAjNDQ0KCzZ8/q4sWLVo+CdtKtWzdFR0crKCiozfsgZAAAtuf1elVSUqKAgADFxMQoKCiIm5wazOfzqaGhQefOnVNJSYkGDRp0zZveXQshAwCwvYaGBnm9XrndbnXr1s3qcdAOQkJCFBgYqH/84x9qaGhQcHBwm/bDxb4AAGO09V/tsKf2+PPkvwgAAGAsTi0BAIx2uvKSLtQ1dNj73dY9SLeHh3TY++HaCBkAgLFOV17SlF/mqb7R22HvGRzYRbk/mdghMbNhwwalpaWpsrLypr+XqQgZAICxLtQ1qL7Rq9RJAzskLE5XXlLWrmJdqGto9fvNnz9fGzdulCQFBgYqNjZW8+bN0zPPPKOuXa/91/B9992nmTNn3vDcHeE3v/mNcnJydPDgQdXU1OjChQsKDw+/6e9LyAAAjHd7eIjienW3eowWzZgxQ+vXr5fH49G2bduUmpqqwMBAZWRkXPN1ISEhCgkx4zTWxYsXNWPGDM2YMeNrf1/tiZC5ASWf1qnO87nVYxiju7Orrf9HAwA3i9PpVFRUlCRp0aJF2rx5s9555x0tXLhQTzzxhN599115PB790z/9k371q19p0KBBkq48tfThhx8qLS1NBw4ckMPh0KBBg7Ru3TqNGTNG//jHP7R48WJ98MEHamhoUP/+/fXSSy/5j+jk5+frqaee0ocffqiIiAilpKTohRde8B8VmjhxouLj4xUcHKz//M//VFBQkBYuXKgVK1a06veYlpYmScrLy2u3z601CJk2Kvm0TpP+/zyrxzDOricnEjMAbnkhISE6f/685s+fr+PHj+udd95RWFiYnn76ac2cOVMfffSRAgMDr3jdQw89pG984xvKzs5WQECACgsL/dulpqaqoaFBu3fvVvfu3fXRRx+pR48ekqTTp09r5syZmj9/vn73u9/p2LFjWrBggYKDg5uFysaNG5Wenq59+/Zpz549mj9/vsaPH6+pU6d2yOfSFoRMG10+EtNR52VNd/m8MkewANzKfD6fcnNztWPHDiUlJWnLli3661//qu985zuSpNdff11ut1tbtmzRvffee8XrT548qaeeekpDhw6VJP+Rm8vrkpOTdeedd0qSBgwY4F/36quvyu12a82aNXI4HBo6dKjOnDmjp59+WsuWLfPfzyU+Pl7Lly/373vNmjXKzc0lZDozu5+XBQBYb+vWrerRo4caGxvl9Xr14IMPau7cudq6davGjRvn365nz54aMmSIPv7446vuJz09XY8++qj+67/+S4mJibr33nt1xx13SJJ+/OMfa9GiRfrLX/6ixMREJScnKz4+XpL08ccfKyEhodmPdRg/frxqa2t16tQpxcbGSpJ/+8uio6NVUVHRrp9Fe+OGeAAA3GSTJk1SYWGhjh8/rkuXLmnjxo1t+llRK1as0NGjR/W9731P77//voYPH67NmzdLkh599FH97//+r370ox/p8OHDGjNmjH79619f1/6/ejrL4XDI6+24r7a3BSEDAMBN1r17dw0cOFCxsbH+i2uHDRumzz//XPv27fNvd/78eRUVFWn48OEt7mvw4MFaunSp/vKXv2ju3Llav369f53b7dbChQv11ltv6Sc/+Yn+4z/+w/9ee/bskc/n82/717/+VaGhoerbt297/3Y7FKeWAADGO115ybj3GTRokGbPnq0FCxZo3bp1Cg0N1c9+9jPdfvvtmj179hXbX7p0SU899ZT++Z//WXFxcTp16pT279+v5ORkSV98aygpKUmDBw/WhQsXtGvXLg0bNkyS9K//+q9avXq1lixZosWLF6uoqEjLly9Xenp6u/38qrKyMpWVlam4uFiSdPjwYYWGhio2NlYRERHt8h5XY2nIZGdnKzs7W5988okkacSIEVq2bJmSkpIkffFVsPz8/Gavefzxx7V27dqOHhUAYEO3dQ9ScGAXZe0q7rD3DA7sotu6B7XLvtavX68nnnhC99xzjxoaGjRhwgRt27btqt9YCggI0Pnz5zVv3jyVl5erV69emjt3rlauXClJampqUmpqqk6dOqWwsDDNmDFDL7/8siTp9ttv17Zt2/TUU09p1KhRioiI0COPPKJnn322XX4fkrR27Vr/LJI0YcIE/+9x/vz57fY+X+Xwffk4Uwd79913FRAQoEGDBsnn82njxo166aWX9D//8z8aMWKEJk6cqMGDB+v555/3v6Zbt24KCwtr9XtUV1fL5XKpqqrqul73dY6crtI9v/5A/98P7uRi31Yo+bROz2w+rK1L7tbI211WjwPAMPX19SopKVFcXJyCg4ObreNnLZnrWn+urf3729IjMrNmzWr2/Oc//7mys7O1d+9ejRgxQtIX4XL5JkIAAHzV7eEhhMUtzDbXyDQ1NenNN99UXV2dEhIS/Mtff/11/f73v1dUVJRmzZql5557Tt26dWtxPx6PRx6Px/+8urr6ps6N61NcUWv1CEbgLsgA7OT111/X448/ftV1/fr109GjRzt4ov/H8pA5fPiwEhISVF9frx49emjz5s3+q7UffPBB9evXTzExMTp06JCefvppFRUV6a233mpxf5mZmc3O0cEeggO/uJgs7Y1CawcxCHdBBmAX3//+95vd7+bLrnY9T0eyPGSGDBmiwsJCVVVV6U9/+pNSUlKUn5+v4cOH67HHHvNvd+eddyo6OlpTpkzRiRMn/DcA+qqMjAylp6f7n1dXV8vtdt/03weuLdoVolU/HKX6Rnvfj8AOuAsyALsJDQ1VaGio1WNcleUhExQUpIEDB0qSRo8erf379+uVV17RunXrrtj2cg0WFxe3GDJOp1NOp/PmDYw2i3ZxDhvAjbHw+ym4Cdrjz9N2N8Tzer3NrnH5ssLCQklf3DIZAHDruHz64uLFixZPgvZ0+c/zRk5PWXpEJiMjQ0lJSYqNjVVNTY1ycnKUl5enHTt26MSJE8rJydHMmTPVs2dPHTp0SEuXLtWECROu+FkQAIDOLSAgQOHh4f6f+9OtW7c23eIf9uDz+XTx4kVVVFQoPDxcAQEBbd6XpSFTUVGhefPm6ezZs3K5XIqPj9eOHTs0depUlZaWaufOnVq9erXq6urkdruVnJzcrjfvAQCY4/KtOOz+QwzReuHh4Td8ixVLQ+a1115rcZ3b7b7irr4AgFuXw+FQdHS0+vTpo8bGRqvHwQ0KDAy8oSMxl1l+sS8AANcjICCgXf4CROdgu4t9AQAAWouQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGMvSkMnOzlZ8fLzCwsIUFhamhIQE/fnPf/avr6+vV2pqqnr27KkePXooOTlZ5eXlFk4MAADsxNKQ6du3r1588UUVFBTowIEDmjx5smbPnq2jR49KkpYuXap3331Xb775pvLz83XmzBnNnTvXypEBAICNdLXyzWfNmtXs+c9//nNlZ2dr79696tu3r1577TXl5ORo8uTJkqT169dr2LBh2rt3r7797W9bMTIAALAR21wj09TUpE2bNqmurk4JCQkqKChQY2OjEhMT/dsMHTpUsbGx2rNnT4v78Xg8qq6ubvYAAACdk+Uhc/jwYfXo0UNOp1MLFy7U5s2bNXz4cJWVlSkoKEjh4eHNto+MjFRZWVmL+8vMzJTL5fI/3G73Tf4dAAAAq1geMkOGDFFhYaH27dunRYsWKSUlRR999FGb95eRkaGqqir/o7S0tB2nBQAAdmLpNTKSFBQUpIEDB0qSRo8erf379+uVV17Rfffdp4aGBlVWVjY7KlNeXq6oqKgW9+d0OuV0Om/22AAAwAYsPyLzVV6vVx6PR6NHj1ZgYKByc3P964qKinTy5EklJCRYOCEAALALS4/IZGRkKCkpSbGxsaqpqVFOTo7y8vK0Y8cOuVwuPfLII0pPT1dERITCwsK0ZMkSJSQk8I0lAAAgyeKQqaio0Lx583T27Fm5XC7Fx8drx44dmjp1qiTp5ZdfVpcuXZScnCyPx6Pp06fr1VdftXJkAABgI5aGzGuvvXbN9cHBwcrKylJWVlYHTQQAAExiu2tkAAAAWouQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxrI0ZDIzMzV27FiFhoaqT58+mjNnjoqKipptM3HiRDkcjmaPhQsXWjQxAACwE0tDJj8/X6mpqdq7d6/ee+89NTY2atq0aaqrq2u23YIFC3T27Fn/4xe/+IVFEwMAADvpauWbb9++vdnzDRs2qE+fPiooKNCECRP8y7t166aoqKiOHg8AANicra6RqaqqkiRFREQ0W/7666+rV69eGjlypDIyMnTx4sUW9+HxeFRdXd3sAQAAOidLj8h8mdfrVVpamsaPH6+RI0f6lz/44IPq16+fYmJidOjQIT399NMqKirSW2+9ddX9ZGZmauXKlR01NgAAsJBtQiY1NVVHjhzRBx980Gz5Y4895v/1nXfeqejoaE2ZMkUnTpzQHXfcccV+MjIylJ6e7n9eXV0tt9t98wYHAACWsUXILF68WFu3btXu3bvVt2/fa247btw4SVJxcfFVQ8bpdMrpdN6UOQEAgL1YGjI+n09LlizR5s2blZeXp7i4uK99TWFhoSQpOjr6Jk8HAADsztKQSU1NVU5Ojt5++22FhoaqrKxMkuRyuRQSEqITJ04oJydHM2fOVM+ePXXo0CEtXbpUEyZMUHx8vJWjAwAAG7A0ZLKzsyV9cdO7L1u/fr3mz5+voKAg7dy5U6tXr1ZdXZ3cbreSk5P17LPPWjAtAACwG8tPLV2L2+1Wfn5+B00DAABMY6v7yAAAAFwPQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYq00hM2DAAJ0/f/6K5ZWVlRowYMANDwUAANAabQqZTz75RE1NTVcs93g8On369A0PBQAA0Bpdr2fjd955x//rHTt2yOVy+Z83NTUpNzdX/fv3b7fhAAAAruW6QmbOnDmSJIfDoZSUlGbrAgMD1b9/f/3yl79st+EAAACu5bpOLXm9Xnm9XsXGxqqiosL/3Ov1yuPxqKioSPfcc0+r95eZmamxY8cqNDRUffr00Zw5c1RUVNRsm/r6eqWmpqpnz57q0aOHkpOTVV5efj1jAwCATqpN18iUlJSoV69eN/zm+fn5Sk1N1d69e/Xee++psbFR06ZNU11dnX+bpUuX6t1339Wbb76p/Px8nTlzRnPnzr3h9wYAAOa7rlNLX5abm6vc3Fz/kZkv++1vf9uqfWzfvr3Z8w0bNqhPnz4qKCjQhAkTVFVVpddee005OTmaPHmyJGn9+vUaNmyY9u7dq29/+9ttHR8AAHQCbTois3LlSk2bNk25ubn69NNPdeHChWaPtqqqqpIkRURESJIKCgrU2NioxMRE/zZDhw5VbGys9uzZc9V9eDweVVdXN3sAAIDOqU1HZNauXasNGzboRz/6UbsN4vV6lZaWpvHjx2vkyJGSpLKyMgUFBSk8PLzZtpGRkSorK7vqfjIzM7Vy5cp2mwsAANhXm47INDQ06Dvf+U67DpKamqojR45o06ZNN7SfjIwMVVVV+R+lpaXtNCEAALCbNoXMo48+qpycnHYbYvHixdq6dat27dqlvn37+pdHRUWpoaFBlZWVzbYvLy9XVFTUVffldDoVFhbW7AEAADqnNp1aqq+v129+8xvt3LlT8fHxCgwMbLZ+1apVrdqPz+fTkiVLtHnzZuXl5SkuLq7Z+tGjRyswMFC5ublKTk6WJBUVFenkyZNKSEhoy+gAAKATaVPIHDp0SHfddZck6ciRI83WORyOVu8nNTVVOTk5evvttxUaGuq/7sXlcikkJEQul0uPPPKI0tPTFRERobCwMC1ZskQJCQl8YwkAALQtZHbt2tUub56dnS1JmjhxYrPl69ev1/z58yVJL7/8srp06aLk5GR5PB5Nnz5dr776aru8PwAAMFub7yPTHnw+39duExwcrKysLGVlZXXARAAAwCRtCplJkyZd8xTS+++/3+aBAAAAWqtNIXP5+pjLGhsbVVhYqCNHjlzxwyQBAABuljaFzMsvv3zV5StWrFBtbe0NDQQAANBabbqPTEv+5V/+pdU/ZwkAAOBGtWvI7NmzR8HBwe25SwAAgBa16dTS3Llzmz33+Xw6e/asDhw4oOeee65dBgMAAPg6bQoZl8vV7HmXLl00ZMgQPf/885o2bVq7DAYAAPB12hQy69evb+85AAAArtsN3RCvoKBAH3/8sSRpxIgR+sY3vtEuQwEAALRGm0KmoqJC999/v/Ly8hQeHi5Jqqys1KRJk7Rp0yb17t27PWcEAAC4qjZ9a2nJkiWqqanR0aNH9dlnn+mzzz7TkSNHVF1drR//+MftPSMAAMBVtemIzPbt27Vz504NGzbMv2z48OHKysriYl+gnRRXcHPJ1uju7Kq4Xt2tHgOARdoUMl6vV4GBgVcsDwwMlNfrveGhgFtZcOAXB0rT3ii0dhCD7HpyIjED3KLaFDKTJ0/WE088oT/84Q+KiYmRJJ0+fVpLly7VlClT2nVA4FYT7QrRqh+OUn0j/yj4OqcrLylrV7HqPJ9bPQoAi7QpZNasWaPvf//76t+/v9xutySptLRUI0eO1O9///t2HRC4FUW7QqweAQCM0KaQcbvdOnjwoHbu3Kljx45JkoYNG6bExMR2HQ4AAOBarutbS++//76GDx+u6upqORwOTZ06VUuWLNGSJUs0duxYjRgxQv/93/99s2YFAABo5rpCZvXq1VqwYIHCwsKuWOdyufT4449r1apV7TYcAADAtVxXyHz44YeaMWNGi+unTZumgoKCGx4KAACgNa4rZMrLy6/6tevLunbtqnPnzt3wUAAAAK1xXSFz++2368iRIy2uP3TokKKjo294KAAAgNa4rpCZOXOmnnvuOdXX11+x7tKlS1q+fLnuueeedhsOAADgWq7r69fPPvus3nrrLQ0ePFiLFy/WkCFDJEnHjh1TVlaWmpqa9G//9m83ZVAAAICvuq6QiYyM1N/+9jctWrRIGRkZ8vl8kiSHw6Hp06crKytLkZGRN2VQAACAr7ruG+L169dP27Zt04ULF1RcXCyfz6dBgwbptttuuxnzAQAAtKhNd/aVpNtuu01jx45tz1kAAACuy3Vd7AsAAGAnhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMZWnI7N69W7NmzVJMTIwcDoe2bNnSbP38+fPlcDiaPWbMmGHNsAAAwHYsDZm6ujqNGjVKWVlZLW4zY8YMnT171v/4wx/+0IETAgAAO2vzT79uD0lJSUpKSrrmNk6nU1FRUR00EQAAMIntr5HJy8tTnz59NGTIEC1atEjnz5+3eiQAAGATlh6R+TozZszQ3LlzFRcXpxMnTuiZZ55RUlKS9uzZo4CAgKu+xuPxyOPx+J9XV1d31LgAAKCD2Tpk7r//fv+v77zzTsXHx+uOO+5QXl6epkyZctXXZGZmauXKlR01IgAAsJDtTy192YABA9SrVy8VFxe3uE1GRoaqqqr8j9LS0g6cEAAAdCRbH5H5qlOnTun8+fOKjo5ucRun0ymn09mBUwEAAKtYGjK1tbXNjq6UlJSosLBQERERioiI0MqVK5WcnKyoqCidOHFCP/3pTzVw4EBNnz7dwqkBAIBdWBoyBw4c0KRJk/zP09PTJUkpKSnKzs7WoUOHtHHjRlVWViomJkbTpk3Tv//7v3PEBQAASLI4ZCZOnCifz9fi+h07dnTgNAAAwDRGXewLAADwZYQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwlqUhs3v3bs2aNUsxMTFyOBzasmVLs/U+n0/Lli1TdHS0QkJClJiYqOPHj1szLAAAsB1LQ6aurk6jRo1SVlbWVdf/4he/0K9+9SutXbtW+/btU/fu3TV9+nTV19d38KQAAMCOulr55klJSUpKSrrqOp/Pp9WrV+vZZ5/V7NmzJUm/+93vFBkZqS1btuj+++/vyFEBAIAN2fYamZKSEpWVlSkxMdG/zOVyady4cdqzZ4+FkwEAALuw9IjMtZSVlUmSIiMjmy2PjIz0r7saj8cjj8fjf15dXX1zBgQAAJaz7RGZtsrMzJTL5fI/3G631SMBAICbxLYhExUVJUkqLy9vtry8vNy/7moyMjJUVVXlf5SWlt7UOQEAgHVsGzJxcXGKiopSbm6uf1l1dbX27dunhISEFl/ndDoVFhbW7AEAADonS6+Rqa2tVXFxsf95SUmJCgsLFRERodjYWKWlpemFF17QoEGDFBcXp+eee04xMTGaM2eOdUMDAADbsDRkDhw4oEmTJvmfp6enS5JSUlK0YcMG/fSnP1VdXZ0ee+wxVVZW6u6779b27dsVHBxs1cgAAMBGLA2ZiRMnyufztbje4XDo+eef1/PPP9+BUwEAAFPY9hoZAACAr0PIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGN1tXoAALhRxRW1Vo9ghO7Ororr1d3qMYB2RcgAMFZw4BcHldPeKLR2EIPsenIiMYNOhZABYKxoV4hW/XCU6hu9Vo9ie6crLylrV7HqPJ9bPQrQrggZAEaLdoVYPQIAC3GxLwAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFi2DpkVK1bI4XA0ewwdOtTqsQAAgE3Y/qdfjxgxQjt37vQ/79rV9iMDAIAOYvsq6Nq1q6KioqweAwAA2JCtTy1J0vHjxxUTE6MBAwbooYce0smTJ6+5vcfjUXV1dbMHAADonGwdMuPGjdOGDRu0fft2ZWdnq6SkRN/97ndVU1PT4msyMzPlcrn8D7fb3YETAwCAjmTrkElKStK9996r+Ph4TZ8+Xdu2bVNlZaX++Mc/tviajIwMVVVV+R+lpaUdODEAAOhItr9G5svCw8M1ePBgFRcXt7iN0+mU0+nswKkAAIBVbH1E5qtqa2t14sQJRUdHWz0KAACwAVuHzJNPPqn8/Hx98skn+tvf/qYf/OAHCggI0AMPPGD1aAAAwAZsfWrp1KlTeuCBB3T+/Hn17t1bd999t/bu3avevXtbPRoAALABW4fMpk2brB4BAADYmK1PLQEAAFwLIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYtv6hkQCA9lVcUWv1CEbo7uyquF7drR4DrUDIAMAtIDjwiwPwaW8UWjuIQXY9OZGYMQAhAwC3gGhXiFb9cJTqG71Wj2J7pysvKWtXseo8n1s9ClqBkAGAW0S0K8TqEYB2x8W+AADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjdbV6AAAA7Ki4otbqEYzQ3dlVcb26W/b+hAwAAF8SHPjFyYq0NwqtHcQgu56caFnMEDIAAHxJtCtEq344SvWNXqtHsb3TlZeUtatYdZ7PLZuBkAEA4CuiXSFWj4BW4mJfAABgLEIGAAAYy4iQycrKUv/+/RUcHKxx48bp73//u9UjAQAAG7B9yLzxxhtKT0/X8uXLdfDgQY0aNUrTp09XRUWF1aMBAACL2T5kVq1apQULFujhhx/W8OHDtXbtWnXr1k2//e1vrR4NAABYzNbfWmpoaFBBQYEyMjL8y7p06aLExETt2bPnqq/xeDzyeDz+51VVVZKk6urqdp2ttqZaXs9FnTh9Thfratp13wAAmOBsZb28nouqralWdbWjXfd9+e9tn893ze1sHTKffvqpmpqaFBkZ2Wx5ZGSkjh07dtXXZGZmauXKlVcsd7vdN2XGZatvym4BADBGwuqbt++amhq5XK4W19s6ZNoiIyND6enp/uder1efffaZevbsKYejfWvRjqqrq+V2u1VaWqqwsDCrx7E1PqvW47NqPT6r68Pn1Xq32mfl8/lUU1OjmJiYa25n65Dp1auXAgICVF5e3mx5eXm5oqKirvoap9Mpp9PZbFl4ePjNGtG2wsLCbon/0NsDn1Xr8Vm1Hp/V9eHzar1b6bO61pGYy2x9sW9QUJBGjx6t3Nxc/zKv16vc3FwlJCRYOBkAALADWx+RkaT09HSlpKRozJgx+ta3vqXVq1errq5ODz/8sNWjAQAAi9k+ZO677z6dO3dOy5YtU1lZme666y5t3779iguA8QWn06nly5dfcXoNV+Kzaj0+q9bjs7o+fF6tx2d1dQ7f132vCQAAwKZsfY0MAADAtRAyAADAWIQMAAAwFiEDAACMRch0MllZWerfv7+Cg4M1btw4/f3vf7d6JNvZvXu3Zs2apZiYGDkcDm3ZssXqkWwrMzNTY8eOVWhoqPr06aM5c+aoqKjI6rFsKTs7W/Hx8f6blSUkJOjPf/6z1WMZ4cUXX5TD4VBaWprVo9jOihUr5HA4mj2GDh1q9Vi2Qsh0Im+88YbS09O1fPlyHTx4UKNGjdL06dNVUVFh9Wi2UldXp1GjRikrK8vqUWwvPz9fqamp2rt3r9577z01NjZq2rRpqqurs3o02+nbt69efPFFFRQU6MCBA5o8ebJmz56to0ePWj2are3fv1/r1q1TfHy81aPY1ogRI3T27Fn/44MPPrB6JFvh69edyLhx4zR27FitWbNG0hd3QXa73VqyZIl+9rOfWTydPTkcDm3evFlz5syxehQjnDt3Tn369FF+fr4mTJhg9Ti2FxERoZdeekmPPPKI1aPYUm1trb75zW/q1Vdf1QsvvKC77rpLq1evtnosW1mxYoW2bNmiwsJCq0exLY7IdBINDQ0qKChQYmKif1mXLl2UmJioPXv2WDgZOpOqqipJX/wFjZY1NTVp06ZNqqur48epXENqaqq+973vNfv/Fq50/PhxxcTEaMCAAXrooYd08uRJq0eyFdvf2Ret8+mnn6qpqemKOx5HRkbq2LFjFk2FzsTr9SotLU3jx4/XyJEjrR7Hlg4fPqyEhATV19erR48e2rx5s4YPH271WLa0adMmHTx4UPv377d6FFsbN26cNmzYoCFDhujs2bNauXKlvvvd7+rIkSMKDQ21ejxbIGQAtEpqaqqOHDnC+flrGDJkiAoLC1VVVaU//elPSklJUX5+PjHzFaWlpXriiSf03nvvKTg42OpxbC0pKcn/6/j4eI0bN079+vXTH//4R05Z/l+ETCfRq1cvBQQEqLy8vNny8vJyRUVFWTQVOovFixdr69at2r17t/r27Wv1OLYVFBSkgQMHSpJGjx6t/fv365VXXtG6dessnsxeCgoKVFFRoW9+85v+ZU1NTdq9e7fWrFkjj8ejgIAACye0r/DwcA0ePFjFxcVWj2IbXCPTSQQFBWn06NHKzc31L/N6vcrNzeUcPdrM5/Np8eLF2rx5s95//33FxcVZPZJRvF6vPB6P1WPYzpQpU3T48GEVFhb6H2PGjNFDDz2kwsJCIuYaamtrdeLECUVHR1s9im1wRKYTSU9PV0pKisaMGaNvfetbWr16terq6vTwww9bPZqt1NbWNvvXTElJiQoLCxUREaHY2FgLJ7Of1NRU5eTk6O2331ZoaKjKysokSS6XSyEhIRZPZy8ZGRlKSkpSbGysampqlJOTo7y8PO3YscPq0WwnNDT0iuusunfvrp49e3L91Vc8+eSTmjVrlvr166czZ85o+fLlCggI0AMPPGD1aLZByHQi9913n86dO6dly5aprKxMd911l7Zv337FBcC3ugMHDmjSpEn+5+np6ZKklJQUbdiwwaKp7Ck7O1uSNHHixGbL169fr/nz53f8QDZWUVGhefPm6ezZs3K5XIqPj9eOHTs0depUq0eDwU6dOqUHHnhA58+fV+/evXX33Xdr79696t27t9Wj2Qb3kQEAAMbiGhkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICx/g8VIKcvd5pgFwAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Заметим, что распределение значений из распределения Пуассона с параметром λ очень схоже с биномиальными распределениями, np которых равно λ, что иллюстрирует правильность теоремы Пуассона."
      ],
      "metadata": {
        "id": "voA3hx7IPaJv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "34. Сгенерировать 100 значений из равномерного на [0;2] распределения. Центрировать и нормировать сумму полученных значений согласно ЦПТ. Повторить эти две процедуры 50 раз, нарисовать гистограмму по полученным 50 значениям. Изобразить на том же графике плотность стандартного нормального закона. Проделать всё тоже самое для 200 и 300 значений сгенерированных значений. Какую теорему иллюстрируют полученные результаты?"
      ],
      "metadata": {
        "id": "iRJW5GieEQqt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from math import sqrt\n",
        "\n",
        "def M(a, b):\n",
        "  return (a + b) / 2\n",
        "\n",
        "def D(a, b):\n",
        "  return ((b - a)**2) / 12\n",
        "\n",
        "def sigm(a, b):\n",
        "  return (sqrt(3) / 6) * (b - a)"
      ],
      "metadata": {
        "id": "PXjTrcGSUYwh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def task(size):\n",
        "  min, max = 0, 2\n",
        "\n",
        "  sample = rng.uniform(low=min, high=max, size=size)\n",
        "  s = sum(sample)\n",
        "  return (s - M(min, max) * size) / (sqrt(size) * sigm(min, max))"
      ],
      "metadata": {
        "id": "wQz_WACPBGj6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "sample_sizes = [50, 200, 300]\n",
        "\n",
        "results = []\n",
        "mu, sigma = 0, 1\n",
        "\n",
        "iter = 0\n",
        "for sz in sample_sizes:\n",
        "  results.append([])\n",
        "  for j in range(sz):\n",
        "    results[iter].append(task(100))\n",
        "  iter += 1"
      ],
      "metadata": {
        "id": "mWWr_4iBWoSc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "count, bins, ignored = plt.hist(results[0], density=True)\n",
        "plt.plot(bins,\n",
        "         1/(sigma * np.sqrt(2 * np.pi)) * np.exp( -(bins - mu)**2 / (2 * sigma**2)),\n",
        "         linewidth=2, color='r')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "kYUcc7R2WwQT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "outputId": "d864284f-5529-4cca-a4e9-dc69decc1ad6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "count, bins, ignored = plt.hist(results[1], density=True)\n",
        "plt.plot(bins,\n",
        "         1/(sigma * np.sqrt(2*np.pi)) * np.exp( -(bins - mu)**2 / (2*sigma**2)),\n",
        "         linewidth=2, color='r')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "_lbQhjwDdqjq",
        "outputId": "0630906f-5037-4cdd-a8b4-7eb36f9a7ee0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "count, bins, ignored = plt.hist(results[2], density=True)\n",
        "plt.plot(bins,\n",
        "         1/(sigma * np.sqrt(2*np.pi)) * np.exp( -(bins - mu)**2 / (2*sigma**2)),\n",
        "         linewidth=2, color='r')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "7Y3X6YMBduuo",
        "outputId": "7027f977-43b5-4196-eac5-a4334d7ac80a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiwAAAGdCAYAAAAxCSikAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABOR0lEQVR4nO3deVhU9f4H8PeAMoDICKEsSiKamimgqES5JolmqZUJXhUlr91o9UebWIKmhZqZLV4pzT2FuqW31FAjsbqiJkioobkRIg6LCiOooMz8/jgywygoAwPfWd6v5znP/Z4zZw6fmecmb87y/cg0Go0GRERERCbMRnQBRERERHfDwEJEREQmj4GFiIiITB4DCxEREZk8BhYiIiIyeQwsREREZPIYWIiIiMjkMbAQERGRyWshugBjUKvVyM/PR+vWrSGTyUSXQ0RERPWg0Whw+fJleHl5wcbmzudQLCKw5Ofnw9vbW3QZRERE1ABnz55Fhw4d7riPRQSW1q1bA5A+sLOzs+BqiIiIqD5UKhW8vb21v8fvxCICS/VlIGdnZwYWIiIiM1Of2zl40y0RERGZPAYWIiIiMnkMLERERGTyGhRYli1bBh8fH9jb2yMoKAgHDhyo1/sSExMhk8kwduxYve0ajQaxsbHw9PSEg4MDQkJCcOLEiYaURkRERBbI4MCSlJSE6OhoxMXFISMjA/7+/ggNDUVhYeEd35eTk4PXX38dAwcOvO21RYsW4ZNPPkFCQgL279+PVq1aITQ0FNeuXTO0PCIiIrJABgeWJUuWYPr06YiMjESPHj2QkJAAR0dHrFq1qs73VFVVYeLEiZg7dy58fX31XtNoNFi6dCneeecdjBkzBn5+fli3bh3y8/OxZcsWgz8QERERWR6DAktlZSXS09MREhKiO4CNDUJCQpCWllbn+9599120a9cO06ZNu+21M2fOQKlU6h1ToVAgKCiozmNWVFRApVLpLURERGS5DAosxcXFqKqqgru7u952d3d3KJXKWt/z22+/4csvv8SKFStqfb36fYYcMz4+HgqFQrtwllsiIiLL1qRPCV2+fBmTJ0/GihUr4ObmZrTjxsTEoLS0VLucPXvWaMcmIiIi02PQTLdubm6wtbVFQUGB3vaCggJ4eHjctv+pU6eQk5ODJ554QrtNrVZLP7hFCxw/flz7voKCAnh6euodMyAgoNY65HI55HK5IaUTERGRGTPoDIudnR0CAwORkpKi3aZWq5GSkoLg4ODb9u/evTsOHz6MzMxM7TJ69GgMHToUmZmZ8Pb2RqdOneDh4aF3TJVKhf3799d6TCIiIrI+BvcSio6OxpQpU9C3b1/0798fS5cuRXl5OSIjIwEAERERaN++PeLj42Fvb4+ePXvqvb9NmzYAoLd9xowZmD9/Pu677z506tQJs2fPhpeX123ztRAREZF1MjiwhIWFoaioCLGxsVAqlQgICEBycrL2ptnc3FzY2Bh2a8ybb76J8vJyPPfccygpKcGAAQOQnJwMe3t7Q8sjIiIiCyTTaDQa0UU0lkqlgkKhQGlpKbs1ExERmQlDfn8bfIaFiHR8Zm4TXYJVyFkwSnQJRCQYmx8SWRONBveUl6Bl1XXRlRARGYRnWIishEyjxspv52HYqd+hhgyFTi4437otzjm3xXlnN+Q7t5WW1tL/XnBUADKZ6LKJiAAwsBBZjXGHUzDs1O8AABto4FF2ER5lF9H7/PFa96+wbYn8m0GmOthIYzecc26H885uuGLn0JwfgYisGAMLkRVwvlaGt/as0a4fdu8M97KLaFd+qc73yKuuo9Ol8+h06Xyd+5TYO908K+OGfOd2N8/S6M7WFDjdgyobW2N+FCKyUgwsRFbg/377Cm5XSgEAW7sPxEtj3gIA2N24DveyC2ivKoSnqhheqiK0VxXB83IRvFTS0rryap3HbXOtDG2ulaFH4ZlaX6+S2aDAyRXnW0shRrr81LbG5Sc3XHJw5qUnIrorBhYiC9e98AwiMqSnma60lOO9oc9qX6ts0RJn23jgbJvbW2tUa11RDi9VETy1YaZGsLm53lJdVet7bTVqeF0uhtflYgTmH6t1n6st5NJZmZv3zpx3drt5+andzaBjvD5kRGS+GFiILJlGg7m7EmCrkXp4fRYchvPObQ06xGV5Kxxv2wrH2/rU+rqNugpu5SVSMKkRbLwuF2nP2rS9UlLn8R1uVKDzxXPofPFc3UVs9ADeew949tm69yEii8bAQmTBRmfvQVDeUQDAaRcvrOz3pNF/htrGFoWt70Fh63uQ6dWt1n3kNyrhcTPQeKmK4aUqlMbabUVodf1a3T9EqQReegkIDQXatzf6ZyAi08fAQmShnCqu4O3dq7Trc0P+hcoWLYXUUtHCDn+7eOFvF6/ad9Bo4FxRXuu9ND0KzqDrhVzg6lUgLg5YubJ5iycik8DAQmShXt6bCPeyiwCAnfc9iD2+gYIrugOZDCp7J6jsnZDdzlfvpTZXVchcGwWUlgKrVwMzZgC3NFUlIsvHmW6JLFDn4rN49uB/AUjzqbz7yD8FV9RwJQ7OQEyMtKJWAzNnii2IiIRgYCGyNBoN5vz0ufbJneUPjkPeHZ4CMguvvAJ06CCNt20DUlOFlkNEzY+BhcjCjDz+Pwz8OxMAcFbhjuVB48QWZAwODsD8+br1N96QzrYQkdVgYCGyIA6V1/DOz19q198dNh0VLeUCKzKiSZOAXr2k8cGDwDffiK2HiJoVAwuRBXlh3zdof7kIAJDaKRC7ugQJrsiIbG2BRYt067NmAZWV4uohombFwEJkITpeysdzB74FAFTatMDckOcsb8r70FBg2DBpfPo0kJAgth4iajYMLESWQKNB3E9fQF51AwCwov+TOONqgROsyWTAwoW69XnzpMedicjiMbAQWYBhpw7gkdMHAQD5rd3wWXCY4IqaUGAg8I9/SOPiYv3LRERksRhYiMyc/EYl4n76Qrv+3tBpuGpnL7CiZjB/PmBnJ40/+gg4d4c+RERkERhYiMzcv/Z/i3tLCwAA/+voh23dBwiuqBl06gS8+KI0rp6yn4gsGgMLkRnrUFqAF/ZJj/det7FFXMjzlnejbV3efhtQKKTx6tXAkSNi6yGiJsXAQmTG3vl5JexvSI/2rgl8Aifd7hVcUTO65x5O2U9kRRhYiMzUoNPpGPFXGgCgqFUbfPzwPwRXJACn7CeyGgwsRGbI7sZ1xKXobrR9f8izKJM7CqxIEE7ZT2Q1GFiIzNCzB/+LzhelJ2MOdOiBzQ8MFVyRQJyyn8gqMLAQmRkPVTFe3psIAKiS2WCONd1oWxtO2U9kFRhYiMzMrNRVaHX9GgBgQ++R+NPdV3BFJoBT9hNZPAYWIjMS/HcWRmf/AgC44OCMDwdOFlyRieCU/UQWj4GFyEy0qLqBOT/pzhwsHDwVKnsngRWZGE7ZT2TRGFiIzERExjZ0K84FAGR63odv/EIEV2SCOGU/kcViYCEyA23LLmHGb18BANSQIfbRKGhk/M/3Npyyn8hi8V88IjMwc89qOFdeAQAk+T2KLM+ugisyYZyyn8giMbAQmbjAvD/x9JGfAQAl9k5YNHiK4IpMHKfsJ7JIDQosy5Ytg4+PD+zt7REUFIQDBw7Uue93332Hvn37ok2bNmjVqhUCAgKwfv16vX2mTp0KmUymt4wYMaIhpRFZFBt1Fd7dpbvRdvHAybjkqBBYkZnglP1EFsfgwJKUlITo6GjExcUhIyMD/v7+CA0NRWFhYa37u7q64u2330ZaWhqysrIQGRmJyMhI7NixQ2+/ESNG4Pz589pl06ZNDftERBbkH3/swAOFpwEAR9v5YmMAg3y9cMp+IotjcGBZsmQJpk+fjsjISPTo0QMJCQlwdHTEqlWrat1/yJAhePLJJ3H//fejc+fOePXVV+Hn54fffvtNbz+5XA4PDw/t4uLi0rBPRGQhXK6U4vVf1mnXYx99HmobW4EVmRlO2U9kUQwKLJWVlUhPT0dIiO5xShsbG4SEhCAtLe2u79doNEhJScHx48cxaNAgvddSU1PRrl07dOvWDVFRUbhw4UKdx6moqIBKpdJbiCzNG7+sQ5trZQCAb3s+gvQOPQRXZGY4ZT+RRTEosBQXF6Oqqgru7u56293d3aFUKut8X2lpKZycnGBnZ4dRo0bh008/xaOPPqp9fcSIEVi3bh1SUlKwcOFC7NmzByNHjkRVVVWtx4uPj4dCodAu3t7ehnwMIpPnd/4vhP+xEwBw2c4BCwZHCq7ITIWGAo88Io05ZT+RWWvRHD+kdevWyMzMRFlZGVJSUhAdHQ1fX18MGTIEABAeHq7dt1evXvDz80Pnzp2RmpqKYdX9QWqIiYlBdHS0dl2lUjG0kMWQadR4d1cCbKABACwdMBFFTrxE2iAymXSWpW9faX3ePGDKFN1jz0RkNgw6w+Lm5gZbW1sUFBTobS8oKICHh0fdP8TGBl26dEFAQABee+01jBs3DvHx8XXu7+vrCzc3N5w8ebLW1+VyOZydnfUWIkvxTNZPCDj/FwDguNu9WNvnccEVmTlO2U9kEQwKLHZ2dggMDERKSop2m1qtRkpKCoKDg+t9HLVajYqKijpfz8vLw4ULF+Dp6WlIeURmz/laGd7as0a7PifkedywbZYToZaNU/YTmT2DnxKKjo7GihUrsHbtWmRnZyMqKgrl5eWIjJSusUdERCCmetImSPeb7Nq1C6dPn0Z2djY+/PBDrF+/HpMmTQIAlJWV4Y033sC+ffuQk5ODlJQUjBkzBl26dEFoaKiRPiaReYj+dQPuuSrdRP5D94FI6+gnuCILwSn7icyewX+6hYWFoaioCLGxsVAqlQgICEBycrL2Rtzc3FzY2OhyUHl5OV544QXk5eXBwcEB3bt3x4YNGxAWFgYAsLW1RVZWFtauXYuSkhJ4eXlh+PDhmDdvHuRyuZE+JpHpu7/wNCYf2g4AuNJSjveGThNckYV5+21g1SqgtFSasn/GDKBnT9FVEVE9yTQajUZ0EY2lUqmgUChQWlrK+1moWfnM3GacA2k0+HrjW+if9ycAYOHgKVj+4DPGObYFyFkwyjgHWrhQN1X/qFHA1q3GOS4RNYghv7/ZS4jIBIz9M1UbVk65tseXfceKLchSccp+IrPFwEIkmFPFFczarZspeu6w51DZoqXAiiwYp+wnMlsMLESCvfK/TWhXfgkAsOO+B/GLb6Dgiiwcp+wnMksMLEQCdSnORWT69wCAay3sMG/YdMEVWQFO2U9klhhYiETRaDD3pwS0VEstKP794DPIU7jf5U1kFJyyn8jsMLAQCfLY8f/h4b+zAAC5Cnd83v8pwRVZkeop+6vNmyc97kxEJouBhUgAx8qreOfnldr1d4c9h4qWnHeoWXHKfiKzwsBCJMCLaV/D63IxAGC3byB+6tJfcEVWilP2E5kNBhaiZtbp4jlMP7AZAFBh2wJzhz0nXaKg5scp+4nMBgMLUXPSaBD30xewU98AAKzo/xRyXNsLLsrKvf02oFBI49WrgSNHxNZDRLViYCFqRo+e3I8hZ9IBAPmt3bDswfGCKyLccw9Q3bBVrdZN3U9EJoWBhaiZyK9XIDZlhXZ9/iP/xFU7e4EVkRan7CcyeQwsRM3k+f3fwru0AADwW0d/bO/2sOCKSMvBQXq0uRqn7CcyOQwsRM2gQ4kSUfv/AwC4bmOLOSH/4o22pmbyZE7ZT2TCGFiImkHszythf0Oa/n114GicdLtXcEV0G07ZT2TSGFiImtiQUwcx/MQ+AEBhKxd88vAEwRVRnThlP5HJYmAhakJ2N64jNuUL7fp7Q59FmdxRYEV0R5yyn8hkMbAQNaFpB7fA91I+AOBAhx74b48hYguiu+OU/UQmiYGFqIl4qorw8t5EAECVzAZxjz7PG23NBafsJzI5DCxETeTt3avgeL0CALC+92PIbucruCKqN07ZT2RyGFiImkDw33/g8WO/AgCKHRVYMnCS4IrIYJyyn8ikMLAQGVmLqhuYu+tz7frCwVOgsncSWBE1CKfsJzIpDCxERjYl/Qd0vZALAMj07Ir/9AoRXBE1GKfsJzIZDCxERtS27CJm/G8jAEANGWY/GgWNjP+ZmS1O2U9kMvgvKZERzUxdjdaVVwEAif6hOOx5n+CKqNE4ZT+RSWBgITKSvnlH8fTR3QCAEnsnfDBosuCKyCg4ZT+RSWBgITICW3UV3t2lm8Z98aAIXHJUCKyIjIpT9hMJx8BCZAT/yPwRPQrPAACOuHfGRv9QwRWRUXHKfiLhGFiIGsn1Sile/2W9dj025HmobWwFVkRNglP2EwnFwELUSG/sWQtFRTkA4D89hyGjw/2CK6Imwyn7iYRhYCFqBP/84wjL2gUAUNk5YuHgqWILoqbFKfuJhGFgIWootRrv7kqADTQAgKUDJqLIyUVwUdTkOGU/kRAMLEQNtWoV/JUnAADH3DpibeDjgguiZsEp+4mEYGAhaojyct0vLQBzHv0XqnijrfXglP1Eza5BgWXZsmXw8fGBvb09goKCcODAgTr3/e6779C3b1+0adMGrVq1QkBAANavX6+3j0ajQWxsLDw9PeHg4ICQkBCcOHGiIaURNY+NG6UnRQBs7TYA++71E1wQNStO2U/U7AwOLElJSYiOjkZcXBwyMjLg7++P0NBQFBYW1rq/q6sr3n77baSlpSErKwuRkZGIjIzEjh07tPssWrQIn3zyCRISErB//360atUKoaGhuHbtWsM/GVFT0WiAZcu0qwkPjhNYDAnDKfuJmpVMo9FoDHlDUFAQ+vXrh88++wwAoFar4e3tjZdffhkz63ktt0+fPhg1ahTmzZsHjUYDLy8vvPbaa3j99dcBAKWlpXB3d8eaNWsQHh5+1+OpVCooFAqUlpbC2dnZkI9DZLi9e4GHHwYgdWMeG7FEcEGWL2fBKNEl1C45GRg5Uhr7+gLZ2brHnonorgz5/W3QGZbKykqkp6cjJCREdwAbG4SEhCAtLe2u79doNEhJScHx48cxaNAgAMCZM2egVCr1jqlQKBAUFFTnMSsqKqBSqfQWomZT4+zKuj4m+ouUmgen7CdqNgYFluLiYlRVVcHd3V1vu7u7O5RKZZ3vKy0thZOTE+zs7DBq1Ch8+umnePTRRwFA+z5DjhkfHw+FQqFdvL29DfkYRA1XUKA79X/PPdjWfaDYekgsTtlP1Gya5Smh1q1bIzMzE7///jvee+89REdHI7URd9XHxMSgtLRUu5w9e9Z4xRLdyZdfAtevS+Np01DRgqf/rR6n7CdqFgYFFjc3N9ja2qKgoEBve0FBATw8POr+ITY26NKlCwICAvDaa69h3LhxiI+PBwDt+ww5plwuh7Ozs95C1ORu3NCd8pfJgOefF1sPmQ5O2U/U5AwKLHZ2dggMDERKSop2m1qtRkpKCoKDg+t9HLVajYqKCgBAp06d4OHhoXdMlUqF/fv3G3RMoia3bRtQfTbvscekadqJAE7ZT9QMDL4kFB0djRUrVmDt2rXIzs5GVFQUysvLERkZCQCIiIhATI0JteLj47Fr1y6cPn0a2dnZ+PDDD7F+/XpMmjQJACCTyTBjxgzMnz8f33//PQ4fPoyIiAh4eXlh7NixxvmURMZQ42Zb7S8nomqcsp+oSbUw9A1hYWEoKipCbGwslEolAgICkJycrL1pNjc3FzY2uhxUXl6OF154AXl5eXBwcED37t2xYcMGhIWFafd58803UV5ejueeew4lJSUYMGAAkpOTYW9vb4SPSGQEf/0F7JKaHMLXV3o6hKim6in7Z87UTtnv0zNKdFUGM9lHyMnqGTwPiyniPCzU5P7v/4ClS6XxBx8AN+cM8pm5TVxNVsRsfolevQp07Qrk5QEAwie8b3azIJvNd00WocnmYSGySuXl0il+ALC3B25e/iS6zS1T9r+VulaaGZmIGo2BhehuNm3Sza0RHi6d+ieqy+TJQM+eAIDe548j4PxfggsisgwMLER3ckvfIN5sS3dlawtER2tXJ2dsFVgMkeVgYCG6k337gMxMadyvH9C3r9ByyEyEhQEuLgCAx4/9CpcrnP2WqLEMfkqIyKrw7IpJMMebm2d1GYLnft8MedUNhGXtYldvokbiGRaiuhQW6voGuboC48eLrYfMyobej2nHkw5th426SmA1ROaPgYWoLl9+CVRWSuNp06QnQIjqKdfFE6mdAgEAHVSFGHI6XXBFROaNgYWoNlVV7BtEjbauj25Ok4gM87usRWRKGFiIarNtG5CbK41HjpRmtyUyUKpvIM4qpFnAh5xJR8dL+YIrIjJfDCxEteHNtmQEahtbfBUwUrs+8dCPAqshMm8MLES3+usvYOdOadypE/sGUaMk+T2KCtuWAIDxh3fB/vo1wRURmScGFqJbVd+7AgBRUdJEYEQNdMlRga33DwQAtLlWhieyfxFcEZF5YmAhqunKFV3fILmcfYPIKNb1vuXmW/YXIjIYAwtRTZs2ASUl0jg8HHBzE1oOWYY/PLsiy6MLAKBXwSn2FyJqAAYWomrsG0RNRSbD+hpnWdhfiMhwDCxE1fbvBw4dksZ9+0q9g4iM5Pv7B6HE3gmA1F/Ilf2FiAzCwEJUjWdXqAlVtJTj616PAgDkVTcwPmuX4IqIzAsDCxEg9Q36+mtp7OoqddslMrINvR+DGjIA7C9EZCgGFiIAWLVK1zfo2WfZN4iaRK6LJ/b49gEg9Rcaevqg4IqIzAcDCxH7BlEz0r/5drvASojMCwML0fbtwN9/S+MRI4DOncXWQxaN/YWIGoaBhYg321IzUtvYYkNvXX+hSYd4loWoPhhYyLqdOAHs2CGNfXykMyxETezrXrr+Qs8c/on9hYjqgYGFrBv7BpEA7C9EZDgGFrJeV65ITwcBUt+gZ58VWw9ZFfYXIjIMAwtZr8REXd+gsDD2DaJmxf5CRIZhYCHrxL5BJBr7CxEZhIGFrNP+/UBGhjQODGTfIBLi+/sH4ZJ9awDsL0R0NwwsZJ3+/W/d+MUXpQnjiJpZRUs5vvbT9RcKy9opuCIi08XAQtanqAhISpLGLi7sG0RCfRUwUttfaOKhH9lfiKgODCxkfW7tG+ToKLYesmrsL0RUPwwsZF2qqoDly3XrUVHiaiG6aV2fx7XjiIxtAishMl0MLGRdfvyRfYPI5Ozp1EfbX2jwmQz2FyKqBQMLWRc+ykwmiP2FiO6uQYFl2bJl8PHxgb29PYKCgnDgwIE6912xYgUGDhwIFxcXuLi4ICQk5Lb9p06dCplMpreMYE8XMraTJ4HkZGncsSMwcuSd9ydqRjX7C43P2sX+QkS3MDiwJCUlITo6GnFxccjIyIC/vz9CQ0NRWFhY6/6pqamYMGECdu/ejbS0NHh7e2P48OE4d+6c3n4jRozA+fPntcumTZsa9omI6sK+QWTCavYXUlSUs78Q0S0MDixLlizB9OnTERkZiR49eiAhIQGOjo5YVd2T5RZfffUVXnjhBQQEBKB79+5YuXIl1Go1UlJS9PaTy+Xw8PDQLi4uLg37RES1ubVv0LRpYushqgX7CxHVzaDAUllZifT0dISEhOgOYGODkJAQpKWl1esYV65cwfXr1+Hq6qq3PTU1Fe3atUO3bt0QFRWFCxcu1HmMiooKqFQqvYXojpKSgEuXpPH48ewbRCbpD69u+MPjPgBSf6He+ccFV0RkOgwKLMXFxaiqqoK7u7vednd3dyiVynod46233oKXl5de6BkxYgTWrVuHlJQULFy4EHv27MHIkSNRVVX7BErx8fFQKBTaxdvb25CPQdaGfYPIjGzo/Zh2PPkQH3EmqtasTwktWLAAiYmJ2Lx5M+zt7bXbw8PDMXr0aPTq1Qtjx47F1q1b8fvvvyM1NbXW48TExKC0tFS7nD17tpk+AZmlAweA9HRp3KcP0L+/2HqI7qBmf6FR7C9EpGVQYHFzc4OtrS0KCgr0thcUFMDDw+OO7128eDEWLFiAnTt3ws/P7477+vr6ws3NDSdPnqz1dblcDmdnZ72FqE7sG0RmhP2FiGpnUGCxs7NDYGCg3g2z1TfQBgcH1/m+RYsWYd68eUhOTkbfvn3v+nPy8vJw4cIFeHp6GlIe0e2Ki/X7BoWHi62HqB7YX4jodgZfEoqOjsaKFSuwdu1aZGdnIyoqCuXl5YiMjAQAREREICYmRrv/woULMXv2bKxatQo+Pj5QKpVQKpUoKysDAJSVleGNN97Avn37kJOTg5SUFIwZMwZdunRBaGiokT4mWa1Vq4CKCmkcGcm+QWQW2F+I6HYGB5awsDAsXrwYsbGxCAgIQGZmJpKTk7U34ubm5uL8+fPa/ZcvX47KykqMGzcOnp6e2mXx4sUAAFtbW2RlZWH06NHo2rUrpk2bhsDAQPz666+Qy+VG+phkldg3iMwY+wsR6ZNpNOb/oL9KpYJCoUBpaSnvZyGdbduAx2/+ox8aqpvl1oh8ZvIXCTUNG3UVUr94DveWSvcMDpn+OXJc2zf5z81ZMOruOxEZiSG/v9lLiCwXH2UmM6a2scVXNfoLTcz8UWA1ROIxsJBlOnVKv2/QY4/deX8iE8T+QkQ6DCxkmRISdNOaP/88+waRWbrkqMAP9w8CIPUXGv0n+wuR9WJgIctz9aqub5CdHfsGkVlbX2Pm24hD7C9E1ouBhSxPUhJw8aI0Hj8eaNtWbD1EjVCzv1BP9hciK8bAQpaHN9uShVnfR/fkDvsLkbViYCHLcuAAcPDmJFu9ewNBQWLrITKCH7oP1OsvdE95idiCiARgYCHLwr5BZIFu7S80/vAuwRURNT8GFrIcxcVAYqI0btMGmDBBaDlExrSh92PsL0RWjYGFLMfq1ewbRBbrbBsPpPoGApD6Cz1yiv2FyLowsJBlYN8gsgK8+ZasGQMLWYbkZODMGWk8fDhw331i6yFqAns69UGuQmo0O/hMBnwunhNcEVHzaSG6AKJqjWkkuOqbOXjk5vifTkH4iU0JyQKpbWyxofdjmJW6GgAw6dB2zB82XXBVRM2DZ1jI7HmXKDHkdDoAIM+5LX7u3FdwRURN55teIdr+Qs8c/on9hchqMLCQ2Zt4aDtsIE1XvjFgJNQ27BtElov9hchaMbCQWZNfr0BYljQnRYVtCyT5DRdcEVHTW1fj5lv2FyJrwcBCZu3xY7/B5dplAMD2bgNwoVUbsQURNYMsz67sL0RWh4GFzNrkQ1u145qPfBJZOj7iTNaGgYXMlt/5vxBw/gQA4Gg7X2R4dRdcEVHzYX8hsjYMLGS2Jmds147X9RnFvkFkVW7tLxSWtVNwRURNi4GFzFKbqyo8cUx6OkIlb4X/9hgsuCKi5lezv9A/MtlfiCwbAwuZpWeyfoL9jUoA0rwU11raC66IqPnp9xcqYn8hsmgMLGR2ZBo1JmXqLgdt6P2YwGqIxNJ7xDlj6x32JDJvDCxkdgafTkfHEiUA4Bef3jjj2l5wRUTi/FKjv9CgnEPsL0QWi4GFzM7kQ7qzK3yUmaxddX+hapNq/PdBZEkYWMisdChRYujN6/R5zm2R0rmf4IqIxPva71H2FyKLx8BCZmVS5o/sG0R0ixIHZ/YXIovHwEJmQ36jEuNv9g2qtGHfIKKa2F+ILB0DC5mNUcd+hetVFQBge/eH2TeIqIYsz67I9NT1F+qTf0xwRUTGxcBCZiMiQ9cvZV3vxwVWQmSaNvTWnWXhzbdkaRhYyCz0On8CAef/AnCzb1B79g0iuhX7C5ElY2Ahs1CzG+363o+xbxBRLSpaypHE/kJkoRhYyOS1uarC6OyafYOGiC2IyIR9xf5CZKEYWMjkjTus6xv0n57DcNWOfYOI6sL+QmSpGhRYli1bBh8fH9jb2yMoKAgHDhyoc98VK1Zg4MCBcHFxgYuLC0JCQm7bX6PRIDY2Fp6ennBwcEBISAhOnDjRkNLIwsg0akw69KN2nX2DiO6O/YXIEhkcWJKSkhAdHY24uDhkZGTA398foaGhKCwsrHX/1NRUTJgwAbt370ZaWhq8vb0xfPhwnDun63exaNEifPLJJ0hISMD+/fvRqlUrhIaG4to1ztZo7QafzoBPyXkAwK8dA3D6ng6CKyIyfXt8A/X6C3VifyGyAAYHliVLlmD69OmIjIxEjx49kJCQAEdHR6xatarW/b/66iu88MILCAgIQPfu3bFy5Uqo1WqkpKQAkM6uLF26FO+88w7GjBkDPz8/rFu3Dvn5+diyZUujPhyZv0k1b7Zl3yCietHIbPTORk7kI85kAQwKLJWVlUhPT0dISIjuADY2CAkJQVpaWr2OceXKFVy/fh2urq4AgDNnzkCpVOodU6FQICgoqM5jVlRUQKVS6S1keTqUKLXX38+1bouULv0FV0RkPr72exTXWtgBYH8hsgwGBZbi4mJUVVXB3d1db7u7uzuUSmW9jvHWW2/By8tLG1Cq32fIMePj46FQKLSLt7e3IR+DzMTEzOQafYNGoIp9g4jqrcTBGT901/UXGvPnHsEVETVOsz4ltGDBAiQmJmLz5s2wt2/4kx4xMTEoLS3VLmfPnjVilWQK5DcqtXNIVNq0QJI/+wYRGWp9H91loYgM9hci82ZQYHFzc4OtrS0KCgr0thcUFMDDw+OO7128eDEWLFiAnTt3ws/PT7u9+n2GHFMul8PZ2VlvIctSs2/Qj90eRnErF8EVEZmfmv2FHig8zf5CZNYMCix2dnYIDAzU3jALQHsDbXBwcJ3vW7RoEebNm4fk5GT07dtX77VOnTrBw8ND75gqlQr79++/4zHJsk3O0N0kuI432xI12Poafbcm1+jHRWRuDL4kFB0djRUrVmDt2rXIzs5GVFQUysvLERkZCQCIiIhATEyMdv+FCxdi9uzZWLVqFXx8fKBUKqFUKlFWVgYAkMlkmDFjBubPn4/vv/8ehw8fRkREBLy8vDB27FjjfEoyKz2VJ9H7/HEAwJ/tOiG9/f2CKyIyX1u7D9D2F3rs+G/sL0Rmq4WhbwgLC0NRURFiY2OhVCoREBCA5ORk7U2zubm5sLHR5aDly5ejsrIS48aN0ztOXFwc5syZAwB48803UV5ejueeew4lJSUYMGAAkpOTG3WfC5mvmn8Fru89in2DiBqhur/Q8we+0/YX+nfweNFlERlMptGY/11YKpUKCoUCpaWlvJ/FjPnM3AbF1cvY/+8psL9RCZWdI4JeXMep+IkaybtEiT2fT4cNNMhzbotB/1oJdR1P3eUs4CVYaj6G/P5mLyEyKTX7Bn3bi32DiIzh1v5Cw079LrgiIsMxsJDJkGnUmFxjRs71vfmXHpGx1Lx5nTffkjliYCGTMejMIfYNImoie3wD8XcbaaoI9hcic8TAQiajZt+gDX3YlZnImDQyG2wI0P13NYn9hcjMMLCQacjJwbCT0nX1/NZu+KlLkOCCiCzPN34hev2FHCrZX4jMBwMLmYbPP2ffIKImVrO/kHNFOUZns78QmQ8GFhLv2jVg5UoAN/sG+YUKLojIctW8+Zb9hcicMLCQeF98ARQXAwCSuz2EIif2DSJqKoc972N/ITJLDCwk1pUrwPvva1cTgsbdYWciMgb2FyJzxMBCYv3738DNTt3buz6EP919BRdEZPm23j+Q/YXI7DCwkDiXLwMLF0pjmQwfDZgoth4iK1HRwg5Jfo8CgLa/EJGpY2AhcT79VHvvCsLDcaJtR7H1EFmRDb0fgxpSY9F/ZP4IG3WV4IqI7oyBhcQoLQUWL5bGNjZAXJzYeoisTF4bD+zu3BcA+wuReWBgITE++gi4dEkaT54MdOsmth4iK7S+t27mW958S6aOgYWa38WLUmABgBYtgNhYsfUQWSn2FyJzwsBCzW/xYkClksaRkYAvnwwiEoH9hcicMLBQ8yoqAj75RBrb2QHvvCO2HiIrd2t/IZSXC66IqHYMLNS8Fi3S/YM4fTpw771i6yGycrf2F8KmTYIrIqodAws1H6USWLZMGsvlwKxZYushIgD6/YXw2WfsL0QmiYGFmk98PHD1qjSOigK8vMTWQ0QAqvsLdZVW/vgD2LJFaD1EtWFgoeaRlwckJEhjR0dg5kyx9RCRnk8fCtOtxMQAN26IK4aoFgws1Dzeew+orJTGL70EuLuLrYeI9KR07o/f2/eQVo4fB9asEVoP0a0YWKjp5eQAX34pjZ2cgDfeEFoOEdVCJsOCIVN163FxUjd1IhPBwEJNb9484Pp1aTxjBuDmJrQcIqpdeocewJgx0kp+vm4KAiITwMBCTevkSWDtWmmsUADR0WLrIaI7e/99qb8XACxYIM1MTWQCGFioac2dC1Td7AL72muAi4vYeojoznr0AKZOlcalpdLTfUQmgIGFmk52NvDVV9LY1RV49VWx9RBR/cyZA9jbS+NPPwXOnhVaDhHAwEJNac4c3QRUb74JODsLLYeI6snbG3j5ZWlcUSHdgEskGAMLNY2sLODrr6Vxu3bSo8xEZD5mzgTatJHGa9cCR48KLYeIgYWaRs2/yGbOBFq1ElcLERnO1VU3waNazVYaJBwDCxlferpuam8vL+D554WWQ0QN9MorQPv20vj774HffhNbD1k1BhYyvthY3XjWLMDBQVwtRNRwDg7Sk37V3nqLjRFJGAYWMq60NGD7dmns7Q38859i6yGixpkyBejeXRrv3Qv88IPYeshqNSiwLFu2DD4+PrC3t0dQUBAOHDhQ575Hjx7F008/DR8fH8hkMixduvS2febMmQOZTKa3dK/+D4TMS817V2bPBuRycbUQUeO1aKE/F0tMjG5uJaJmZHBgSUpKQnR0NOLi4pCRkQF/f3+EhoaisLCw1v2vXLkCX19fLFiwAB4eHnUe94EHHsD58+e1y2+8Vmp+fv0V2LVLGvv66iafIiLzNmYMEBwsjf/8E1i3Tmw9ZJUMDixLlizB9OnTERkZiR49eiAhIQGOjo5YtWpVrfv369cPH3zwAcLDwyG/w1/bLVq0gIeHh3ZxY78Z86LRSGdUqsXGAi1biquHiIxHJgMWLtStx8YCV6+Kq4eskkGBpbKyEunp6QgJCdEdwMYGISEhSEtLa1QhJ06cgJeXF3x9fTFx4kTk5uY26njUzH7+GdizRxp37QpMnCi2HiIyroEDgccfl8Z5ecBnn4mth6yOQYGluLgYVVVVcHd319vu7u4OpVLZ4CKCgoKwZs0aJCcnY/ny5Thz5gwGDhyIy5cv17p/RUUFVCqV3kIC3Xp2JS5Ouu5NRJYlPl4621I9vnRJbD1kVUziKaGRI0fimWeegZ+fH0JDQ7F9+3aUlJTg6+qZUm8RHx8PhUKhXby9vZu5YtKTnCw9HQRIjdPCwsTWQ0RNo2dPICJCGl+6pH+ZiKiJGRRY3NzcYGtri4KCAr3tBQUFd7yh1lBt2rRB165dcfLkyVpfj4mJQWlpqXY5y8Zc4mg0+vOuzJ0L2NqKq4eImta77+qe/vv4Y+nyEFEzMCiw2NnZITAwECkpKdptarUaKSkpCK6+g9wIysrKcOrUKXh6etb6ulwuh7Ozs95Cgnz/PXDwoDT29weeekpsPUTUtO69F3jxRWl87Zr+xHJETcjgS0LR0dFYsWIF1q5di+zsbERFRaG8vByRkZEAgIiICMTExGj3r6ysRGZmJjIzM1FZWYlz584hMzNT7+zJ66+/jj179iAnJwd79+7Fk08+CVtbW0yYMMEIH5GajFqtf3bl3XcBG5O4ykhETWnWLF339VWrgOxssfWQVTD4zsiwsDAUFRUhNjYWSqUSAQEBSE5O1t6Im5ubC5sav7Ty8/PRu3dv7frixYuxePFiDB48GKmpqQCAvLw8TJgwARcuXEDbtm0xYMAA7Nu3D23btm3kx6Mm9e23UldmAOjXD3jiCbH1EFHzuOceqTHirFm6xoibN4uuiiycTKMx/8YQKpUKCoUCpaWlvDzUXKqqgF69dH9Z/fgjMGJEow7pM3ObEQojosbIWTCqfjteuQJ06QKcPy+t792rm1yOqJ4M+f3N8/fUMImJurDy0ENAaKjYeoioeTk6AnPm6NbZGJGaGAMLGe7GDf0b7ebN083NQETW49lnpYkiAak1R3XjU6ImwMBChlu/HjhxQhoPGQI88ojQcohIkBYtgPff163PnMnGiNRkGFjIMJWV0tNA1ebNE1cLEYn31FNA//7S+MgRYMMGsfWQxWJgIcOsXg3k5Ejj4cOBAQOElkNEgslkwKJFuvXYWGl+FiIjY2Ch+rt2DZg/X7fOsytEBACDBwMjR0rj3Fzg3/8WWw9ZJAYWqr+VK3XTcD/+uO40MBFRzcaI770HlJaKrYcsDgML1c/Vq/o319W8j4WIyN8fmDRJGl+8qH+ZiMgIGFiofpYv100Q9dRTQI3Zi4mIAEh/yNjZSeOPPgLy88XWQxaFgYXurqwMWLBAGstkbHZGRLXz8QFeeEEaX73KM7FkVAwsdHeffQYUFUnj8eOBnj3F1kNEpuvtt4HWraXxypXA8eNi6yGLwcBCd6ZSAR98II1tbPSn4iYiupWbG/Dmm9K4qkoKMERGwMBCd7Z0qXQDHQBMnAh07y60HCIyA//3f4C7uzT+9ltg/36x9ZBFYGChul26BCxZIo1tbaUJoYiI7qZVKyAuTrfOxohkBAwsVLcPP9TNpTB1qtRKnoioPv75T92/GXv2AMnJYushs8fAQrUrLgY+/lgat2wJzJ4tth4iMi8tW97eGFGtFlcPmT0GFqrdokXS48yA9JdSx45i6yEi8zNuHNC3rzTOygI2bhRbD5m1FqILIBOkVEqPMgOAXM67/ImsiM/MbUY9XnCXJ7Hp4EEAQN6Lr+GRTCdUtmhp1J+Rs2CUUY9HpolnWOh2CxZIkz4BwPPPA+3bi62HiMxWWkd/7OnUBwDQQVWIiZnbBVdE5oqBhfTl5QEJCdLYwUG67kxE1AiLBk/Rjl/amwSniisCqyFzxcBC+t5/H6iokMYvvQR4eIith4jM3lH3ztjSYzAA4J6rKkw/8J3gisgcMbCQzt9/S1NpA4CTk262SiKiRvpw4GRU2ki3TU7/fTPall0SXBGZGwYW0pk/H7h+XRq/+qo0xTYRkRGcbeOBr3qPBAA4Xq/AK3s3Ca6IzA0DC0lOnQJWr5bGCgXw2mti6yEii/NZcBjK7BwAAOF/7IDPxXOCKyJzwsBCknfflRqVAUB0NODiIrYeIrI4F1q1wYp+TwIAWqqr8PqvGwRXROaEgYWAY8eADTf/4XB1BWbMEFoOEVmulf3GosixDQDg8WO/otf5E2ILIrPBwELA3Lm6KbPfeANwdhZbDxFZrHK5Iz55OFy7PnPPajZGpHphYLF2R44ASUnSuG1b6VFmIqImlOgfir/bSFMmPPx3FgbmHBJcEZkDBhZrFxen++vmrbekx5mJiJrQdduWWDxwsnb9rT1rIdOwMSLdGQOLNTt0CPju5gROHh5AVJTYeojIamy9fyAOu3cGAPQsOIUnsn8VXBGZOgYWaxYbqxvPmgU4OoqrhYisikZmg4WDp2rXX/t1PVpWXRdXEJk8BhZrtX8/sHWrNO7QAZg+XWw9RGR1fuvUG792DAAAdCxRYkJmstiCyKQxsFirmmdX3nkHsLcXVwsRWa2FQ6Zqx6/sTUQrNkakOjCwWKPffgN27pTGPj5AZKTQcojIeh3x6IIfug8EALhdKcX03zcLrohMVYMCy7Jly+Dj4wN7e3sEBQXhwIEDde579OhRPP300/Dx8YFMJsPSpUsbfUxqpNmzdePYWMDOTlwtRGT1Fg+ajOs2tgCAf/6+BW7lbIxItzM4sCQlJSE6OhpxcXHIyMiAv78/QkNDUVhYWOv+V65cga+vLxYsWAAPDw+jHJMa4eefgdRUaXzffcDkyXfcnYioqf3t4oVN/iMAAE6VV/HS3iTBFZEpMjiwLFmyBNOnT0dkZCR69OiBhIQEODo6YtWqVbXu369fP3zwwQcIDw+HXC43yjGpgTQa/bMrcXFAixbi6iEiuunTh8JR3lK6l25i5o+499J5wRWRqTEosFRWViI9PR0hISG6A9jYICQkBGlpaQ0qoCmOSXXYsQPYu1ca9+gBhIffeX8iomZS5OSClTUaI77Gxoh0C4MCS3FxMaqqquDu7q633d3dHUqlskEFNOSYFRUVUKlUegvdxa1nV+bMAWxthZVDRHSrFf2fxAUHqZfZmOw9eEB5UnBFZErM8imh+Ph4KBQK7eLt7S26JNO3dStw8KA09vMDnn5abD1ERLcokzvi04d0Z37f2rNWYDVkagwKLG5ubrC1tUVBQYHe9oKCgjpvqG2KY8bExKC0tFS7nD17tkE/22qo1frzrrz7LmBjllmViCzcxoCRyFVIZ9wH5RzCwzmZYgsik2HQby07OzsEBgYiJSVFu02tViMlJQXBwcENKqAhx5TL5XB2dtZb6A42bwYyM6Vx377A6NFCyyEiqktli5b4cOAk7fpbe9awMSIBaMAloejoaKxYsQJr165FdnY2oqKiUF5ejsibk49FREQgJiZGu39lZSUyMzORmZmJyspKnDt3DpmZmTh58mS9j0mNUFUlPQ1U7d13AZlMXD1ERHfxfY/B+LNdJwCAn/IkHjv2P8EVkSkw+JnWsLAwFBUVITY2FkqlEgEBAUhOTtbeNJubmwubGpcb8vPz0bt3b+364sWLsXjxYgwePBipN+cDudsxqRG+/ho4elQaBwcDI0aIrYeI6C40MhssGDwV676R/th645d12NE1GDdsOQ2DNZNpNBqN6CIaS6VSQaFQoLS0lJeHarpxA3jgAeCvv6T1XbuAGo+PmxqfmdtEl0BEpkKjwcbEt/FQbhYA4J1Ho7Chz6had81ZUPt2Mn2G/P7mnZeW7KuvdGFl0CBg2DCx9RAR1ZdMhgU1GiO+uncTHCuviquHhGNgsVTXr0v3q1SbN4/3rhCRWcny7Ipt3R4GALQtL8G037eILYiEYmCxVGvWAKdPS+OQEOkMCxGRmVk8KAI3ZNKvqucOfAfXK6WCKyJRGFgsUUWFdEalWs0xEZEZOePaHon+oQCA1myMaNUYWCzRypVA9WR6jz0GPPig2HqIiBrh44cn4EpLqXnupEPb0aGkYa1gyLwxsFiay5eB99/Xrde8j4WIyAwVObniy75jAQB26huI/u0rsQWREAwslqSiAnjqKSA/X1ofOxYIDBRaEhGRMXwR9BQu3myMOPZoKnoUnBZcETU3zsJjKaqqgIgI4KefAACl8lYY23YkznBuEyKyAJflrbAseDxm/7wSNtDgzT1rMXX8XNFlUTPiGRZLoNEAL78szWoLAA4OiBw3B2dc24uti4jIiNb3HoU853YAgCFn0hH8d5bgiqg5MbBYgrlzgeXLpbGtLfCf/yCjw/1iayIiMrLbGyOulv5gI6vAwGLuPvtMCizV1qyRngwiIrJA/+0xGNltfQAAAedPYORxNka0Fgws5iwxEXjlFd36Rx8BkybVvT8RkZlT29hi4eAp2vXXf10vzexNFo+BxVzt3CndZFt9OnTWLGDGDKElERE1h1Tfvtjn3RMA0PniOWDVKsEVUXNgYDFH+/cDTz6p+6ti+nRg/nyxNRERNReZDAsHT9Wtx8UBOTmiqqFmwsBibrKzpXtUrlyR1p96Srrhlo0NiciKHGrfHT92fUhaKSgAhgxhaLFwDCzmJDcXGD4cuHhRWh86FPjqK+nJICIiKzN7eBROunaQVv7+Gxg8GDhzRmxR1GQYWMxFcTEQGgrk5UnrffoAW7YA9vZCyyIiEqW4lQsmTIgHuneXNuTmSmdaGFosEgOLOSgrA0aNAo4dk9a7dAF+/BFwdhZbFxGRYEVOLsDu3cD9N+eeYmixWAwspq66P9CBA9K6pyewaxfQrp3YuoiITIWHB/Dzz7eHltPsN2RJ2EuoHnwE9eOxUVfh4x8W44ljvwKQ+gONH/k2jiccBXBUSE1ERCbJw0M60zJ0qPRwQm6uNN69G/D1FV0dGQHPsJgqjQZzfvpCG1autpDj2XFxOH5zhkciIrqFu3vtl4d4psUiMLCYqFf/twkRh6QzOzdkNnhh7Eykd+ghuCoiIhN3a2g5e5ahxUIwsJigSRnb8H//26hdf+OxGdjduZ/AioiIzEh1aOlx84+86tBy6pTQsqhxGFhMzBN/7sG7uxK06/Me+Sc293xEYEVERGbI3V26EbdmaBk6lKHFjDGwmJCBZzLw4baPYAOpP9CyB5/Bl/3Gii2KiMhcMbRYFAYWExGQfxwJm9+HnfoGAGCT33B8MChCcFVERGaOl4csBgOLCehcfBar/jMXra5fAwAkdw3GO6Evsj8QEZExtGunH1ry8hhazBADi2CeqiKs/3o2XK+qAABp9/bCq0+8gSob9gciIjKa6tDywAPSenVoOXlSaFlUfwwsArW5qsL6pNnwulwMADji3hnTn5qNihZ2gisjIrJA7dpJ97TUDC1DhzK0mAkGFkEcK69izTdz0OWi1MzwjIsnpj4zB2VyR8GVERFZsOrQ0rOntM4zLWaDU/ML0LLqOhI2v4+A838BAAqcXDF5/DwUt3IRXBkRkflpSPuUe4bMxFfKt9G9+G/g3Dmc7/0gwv8Rj79dvJqgwtvlLBjVLD/HkvAMSzOTadRYsnUJBuUcAiD1B4oY/y7y2ngIroyIyHpcaNUG/5jwPo65dQQAeJZdQOLGGHS8lC+4MqoLA0tz0mgw56fPtf2BrrWww7RxsewPREQkwEVHRa2hxefiOcGVUW0YWJrRK3sTMSVD1x8oamwMDnZ4QHBVRETWq7bQsmnTLIYWE9SgwLJs2TL4+PjA3t4eQUFBOHDgwB33/+abb9C9e3fY29ujV69e2L59u97rU6dOhUwm01tGjBjRkNJM1qRD2xH921fa9Tcfe5X9gYiITEB1aMm+ebbbs+wCEjfxTIupMTiwJCUlITo6GnFxccjIyIC/vz9CQ0NRWFhY6/579+7FhAkTMG3aNBw6dAhjx47F2LFjceTIEb39RowYgfPnz2uXTZs2NewTmaBR2b/i3Z3Ltevzhk7Ddz2HCayIiIhquuiowMTw97ShxaPsIkOLiTE4sCxZsgTTp09HZGQkevTogYSEBDg6OmLVqlW17v/xxx9jxIgReOONN3D//fdj3rx56NOnDz777DO9/eRyOTw8PLSLi4tlPDEz4MwhfLT1Q21/oH8/OA5f9n9ScFVERHSrukJLJ4YWk2BQYKmsrER6ejpCQkJ0B7CxQUhICNLS0mp9T1pamt7+ABAaGnrb/qmpqWjXrh26deuGqKgoXLhwoc46KioqoFKp9BZT5J9/HJ9vfk/bHyjRbzgWDZoiuCoiIqrLRUcF/nFLaNnE0GISDAosxcXFqKqqgru7u952d3d3KJXKWt+jVCrvuv+IESOwbt06pKSkYOHChdizZw9GjhyJqqqqWo8ZHx8PhUKhXby9vQ35GM2i84WzWF2jP9CO+x7E2+wPRERk8i4xtJgkk3hKKDw8HKNHj0avXr0wduxYbN26Fb///jtSU1Nr3T8mJgalpaXa5ezZs81b8F14qoqwLilW2x9on3dPvDL6TfYHIiIyE7WFFl4eEsugwOLm5gZbW1sUFBTobS8oKICHR+0Tn3l4eBi0PwD4+vrCzc0NJ+uYKlkul8PZ2VlvMRVtrqqw7utYtL9cBAA42s4X059mfyAiInNza2hxZ2gRyqDAYmdnh8DAQKSkpGi3qdVqpKSkIDg4uNb3BAcH6+0PALt27apzfwDIy8vDhQsX4OnpaUh5wjlWXsXqb+bivgvSGZ+cNp6YMn4uLstbCa6MiIgaojq0/NmuEwBdaPG9kCe4Mutj8CWh6OhorFixAmvXrkV2djaioqJQXl6OyMhIAEBERARiYmK0+7/66qtITk7Ghx9+iGPHjmHOnDk4ePAgXnrpJQBAWVkZ3njjDezbtw85OTlISUnBmDFj0KVLF4SGhhrpYza96v5Avc8fBwAUtnLB5DD2ByIiMneXHBWYGDZfL7RsSpzF0NLMDA4sYWFhWLx4MWJjYxEQEIDMzEwkJydrb6zNzc3F+fPntfs/9NBD2LhxI7744gv4+/vjP//5D7Zs2YKeNztl2traIisrC6NHj0bXrl0xbdo0BAYG4tdff4VcLjfSx2xaMo0aH277SNsfSHWzP9BZ9gciIrIItZ1pYWhpXjKNRqMRXURjqVQqKBQKlJaWNsn9LHfsBHqzP9DUjK0ApP5Ak8Lmccp9IiIL1OaqChsT30aPwjMApLPp4RPicfqeDgYdh92aJYb8/jaJp4TM2St7E7Vh5YbMBi+MmcmwQkRkoUocnPGP8PdwtJ0vAKBd+SXe09JMGFgaobb+QD936S+wIiIiamolDs6YGD7/ttDS+YJpTbFhaRhYGujW/kDzhz7L/kBERFaittCyadMshpYmxMDSAA/nZOr1B1oeNA4r+z8luCoiImpO1aHliHtnAAwtTY2BxUB+5//CF9/N1/YHSur1KBYOZn8gIiJrVOLgjIlh+qGFl4eaBgOLATpfOIs138zR6w80a8RL7A9ERGTFSh1a64WWtuUlUmgpZmgxJgaWevJQFbM/EBER1arW0JLI0GJMDCz10OaqCuu/ns3+QEREVCeGlqbFwHI35eXsD0RERPVSHVoO3xJauhTnCq7M/DGw3EllJfD00+wPRERE9Vbq0BqTbgktmxJnMbQ0EgPLnfzrX8COHQDYH4iIiOqv1tCyiaGlMRhY7mTyZMDJCdda2GHa07Nx7GbTKyIiorspdWiNieHv6ULLFYaWxmBguZNHHgF270bU2Bj87t1TdDVERGRmVPZOmBj+HrI8ugDQhRb8+afgyswPA8vd9O2L3Z37ia6CiIjMlMreCZPC5uuFFvTrBzz7LLB3L6DRiC3QTDCwEBERNbFbQwuuXAFWrwYefhh44AFgyRKgqEhskSZOptGYf7RTqVRQKBQoLS2Fs7Oz0Y/vM3Ob0Y9JRETWx/laGf7vt6/w9JGf4VxRrvdapU0L7LzvQST5D8dvPgHQyEzrnELOglFGP6Yhv78ZWOqBgYWIiIzJ/vo1jDy+F+FZOxF09shtr+c5t8M3vULwjV8I8p3bCajwdgwsRsDAQkRE5sr3Qh7GH96Fpw+nSPe31KCGDL906oNE/+FI6dIf121biikSDCxGwcBCRETmrkXVDQw7dQBhf+zE4DMZsNWo9V4vdlTg257D8LXfozh1j3ez18fAYgQMLEREZEk8VMUYd+QnhGXtgndpwW2v/96+B5L8h2NbtwG4amffLDUxsBgBAwsREVkimUaNh/7OQvgfOzD8RBrkVTf0Xr9s54DvewxGol8oDnt0AWSyJqtFdGBpYfSfTkREREahkdngfz4B+J9PAFyulOLJo6kIy9qBbjdny21deRUTM5MxMTMZf7brhES/4djywFCo7J0EV258PMNSDzzDQkREJkOjQe/84wjL2oknsn9Bq+vX9F6usG2J7d0extd+w7Hv3p5Gezxa9BkWBpZ6YGAhIiJT1KriCkYd+w3hWTvQJ//4ba/ntPHE136P4pteIShycm3Uz2JgMQIGFiIisnZdi3IQlrULTx35GS7XLuu9dkNmg92d+yHRfzhSffuiysbW4OMzsBgBAwsREZHE7sZ1DD+RhvFZuzAo59Btrxc4ueKbXiH4utejyHXxrPdxGViMgIGFiIjodh1KlHjm8E8Yn7ULnmUXbnt9771+SPQfjh1dH0JFC7s7HouBxQgYWIiIiOpmo67CoDMZCM/aiWEnD6Clukrv9RJ7J2x+YCiS/IbjWLtOtR5DdGDhY81EREQWTm1ji9TO/ZDauR/all3CU0dTEPbHTvheygcAtLlWhsj0HxCZ/gMyPe9Dkl8ofrh/EMrkjoIr1+EZlnrgGRYiIrI4Gg365x1F2B87MOr4/2B/o1Lv5Sst5djWbSAS/Ycjvf39yFn4uNFL4CUhI2NgISIiS+Z8rQyjs39B2B870Kvg1G2vn3TtgC6zZgAREUDbtkb7uQwsRsbAQkRE1uIB5UmEZe3C2D9T4VxRrv/i668DH3xgtJ/FwGJkDCxERGRt7K9fw8jjexGetRNBZ49IG48dA7p1M9rP4E23RERE1CjXWtpjc89HsLnnI+h08Rx2+183algxVIMaDCxbtgw+Pj6wt7dHUFAQDhw4cMf9v/nmG3Tv3h329vbo1asXtm/frve6RqNBbGwsPD094eDggJCQEJw4caIhpREREZGRnXFtD7z4otAaDA4sSUlJiI6ORlxcHDIyMuDv74/Q0FAUFhbWuv/evXsxYcIETJs2DYcOHcLYsWMxduxYHDlyRLvPokWL8MknnyAhIQH79+9Hq1atEBoaimvXrtV6TCIiIrIuBt/DEhQUhH79+uGzzz4DAKjVanh7e+Pll1/GzJkzb9s/LCwM5eXl2Lp1q3bbgw8+iICAACQkJECj0cDLywuvvfYaXn/9dQBAaWkp3N3dsWbNGoSHh9+1Jt7DQkRE1LTMauK4yspKpKenIyYmRrvNxsYGISEhSEtLq/U9aWlpiI6O1tsWGhqKLVu2AADOnDkDpVKJkJAQ7esKhQJBQUFIS0urNbBUVFSgoqJCu15aWgpA+uBNQV1xpUmOS0REZC6a4nds9THrc+7EoMBSXFyMqqoquLu76213d3fHsWPHan2PUqmsdX+lUql9vXpbXfvcKj4+HnPnzr1tu7e3d/0+CBERERlEsbTpjn358mUoFIo77mOWTwnFxMTonbVRq9W4ePEi7rnnHshkMoGVGUalUsHb2xtnz55tkktZxO+4qfH7bXr8jpsWv9+md6fvWKPR4PLly/Dy8rrrcQwKLG5ubrC1tUVBQYHe9oKCAnh4eNT6Hg8PjzvuX/2/BQUF8PT01NsnICCg1mPK5XLI5XK9bW3atDHko5gUZ2dn/ofSxPgdNy1+v02P33HT4vfb9Or6ju92ZqWaQU8J2dnZITAwECkpKdptarUaKSkpCA4OrvU9wcHBevsDwK5du7T7d+rUCR4eHnr7qFQq7N+/v85jEhERkXUx+JJQdHQ0pkyZgr59+6J///5YunQpysvLERkZCQCIiIhA+/btER8fDwB49dVXMXjwYHz44YcYNWoUEhMTcfDgQXzxxRcAAJlMhhkzZmD+/Pm477770KlTJ8yePRteXl4YO3as8T4pERERmS2DA0tYWBiKiooQGxsLpVKJgIAAJCcna2+azc3NhY2N7sTNQw89hI0bN+Kdd97BrFmzcN9992HLli3o2bOndp8333wT5eXleO6551BSUoIBAwYgOTkZ9vb2RviIpksulyMuLu62y1tkPPyOmxa/36bH77hp8fttesb6ji2ilxARERFZtgZNzU9ERETUnBhYiIiIyOQxsBAREZHJY2AhIiIik8fAYiJycnIwbdo0dOrUCQ4ODujcuTPi4uJQWVkpujSL8d577+Ghhx6Co6OjWU80aEqWLVsGHx8f2NvbIygoCAcOHBBdksX45Zdf8MQTT8DLywsymUzbf42MIz4+Hv369UPr1q3Rrl07jB07FsePHxddlsVYvnw5/Pz8tJPFBQcH48cff2zUMRlYTMSxY8egVqvx+eef4+jRo/joo4+QkJCAWbNmiS7NYlRWVuKZZ55BVFSU6FIsQlJSEqKjoxEXF4eMjAz4+/sjNDQUhYWFokuzCOXl5fD398eyZctEl2KR9uzZgxdffBH79u3Drl27cP36dQwfPhzl5eWiS7MIHTp0wIIFC5Ceno6DBw/ikUcewZgxY3D06NEGH5OPNZuwDz74AMuXL8fp06dFl2JR1qxZgxkzZqCkpER0KWYtKCgI/fr1w2effQZAmvXa29sbL7/8MmbOnCm4Ossik8mwefNmTqbZhIqKitCuXTvs2bMHgwYNEl2ORXJ1dcUHH3yAadOmNej9PMNiwkpLS+Hq6iq6DKLbVFZWIj09HSEhIdptNjY2CAkJQVpamsDKiBqmtLQUAPhvbhOoqqpCYmIiysvLG9Vyxyy7NVuDkydP4tNPP8XixYtFl0J0m+LiYlRVVWlnuK7m7u6OY8eOCaqKqGHUajVmzJiBhx9+WG8Wdmqcw4cPIzg4GNeuXYOTkxM2b96MHj16NPh4PMPSxGbOnAmZTHbH5dZ/4M+dO4cRI0bgmWeewfTp0wVVbh4a8v0SEdX04osv4siRI0hMTBRdikXp1q0bMjMzsX//fkRFRWHKlCn4888/G3w8nmFpYq+99hqmTp16x318fX214/z8fAwdOhQPPfSQtkEk1c3Q75eMw83NDba2tigoKNDbXlBQAA8PD0FVERnupZdewtatW/HLL7+gQ4cOosuxKHZ2dujSpQsAIDAwEL///js+/vhjfP755w06HgNLE2vbti3atm1br33PnTuHoUOHIjAwEKtXr9ZrIkm1M+T7JeOxs7NDYGAgUlJStDeCqtVqpKSk4KWXXhJbHFE9aDQavPzyy9i8eTNSU1PRqVMn0SVZPLVajYqKiga/n4HFRJw7dw5DhgxBx44dsXjxYhQVFWlf41+sxpGbm4uLFy8iNzcXVVVVyMzMBAB06dIFTk5OYoszQ9HR0ZgyZQr69u2L/v37Y+nSpSgvL0dkZKTo0ixCWVkZTp48qV0/c+YMMjMz4erqinvvvVdgZZbhxRdfxMaNG/Hf//4XrVu3hlKpBAAoFAo4ODgIrs78xcTEYOTIkbj33ntx+fJlbNy4EampqdixY0fDD6ohk7B69WoNgFoXMo4pU6bU+v3u3r1bdGlm69NPP9Xce++9Gjs7O03//v01+/btE12Sxdi9e3et/3+dMmWK6NIsQl3/3q5evVp0aRbh2Wef1XTs2FFjZ2enadu2rWbYsGGanTt3NuqYnIeFiIiITB5vkiAiIiKTx8BCREREJo+BhYiIiEweAwsRERGZPAYWIiIiMnkMLERERGTyGFiIiIjI5DGwEBERkcljYCEiIiKTx8BCREREJo+BhYiIiEweAwsRERGZvP8HXVkVY2Ds14wAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Вывод:**\n",
        "\n",
        " Распределение средних значений выборок из равномерного распределения является приблизительно нормальным, если размер выборки достаточно велик.\n",
        "\n",
        "Именно об этом говорит ЦПТ, поэтому можно сказать, что приведенные графики ее иллюстрируют."
      ],
      "metadata": {
        "id": "HOwvyT7bRno6"
      }
    }
  ]
}