{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Central Limit Theorem"
      ],
      "id": "460fe1d0-3897-465b-9c9a-9dc615f83823"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy as sp"
      ],
      "id": "983d657f-1b51-4b34-8468-0fb81d920dfc"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Suppose $X_1, \\ldots, X_N$ are random variables from any distribution\n",
        "with common location $\\mathbb{E}[X] = \\mu$ and common variance\n",
        "$\\mathbb{V}[X] = \\sigma^2 < \\infty$, then a properly shifted and scaled\n",
        "mean of the random variable approximately follows a standard Normal\n",
        "distribution:\n",
        "\n",
        "$$\\frac{\\frac{1}{N}\\sum_n^N X_n - \\mu}{\\sqrt{\\sigma^2 / N}} \\sim \\text{Normal}(0, 1)$$.\n",
        "\n",
        "The approximation improves as $N \\to \\infty$."
      ],
      "id": "0bd076f6-0c87-4606-8dec-718b2ca7e4da"
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {},
      "outputs": [],
      "source": [
        "K = 10\n",
        "p = 0.75\n",
        "N = 1000\n",
        "B = sp.stats.binom(K, p)\n",
        "R = 10000\n",
        "means = np.zeros(R)\n",
        "for r in range(R):\n",
        "    x = B.rvs(size = N)\n",
        "    means[r] = np.mean(x)"
      ],
      "id": "8347692e-6e42-4f56-82e9-e206f4829d1a"
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhYAAAGdCAYAAABO2DpVAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90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\nkhEWAEAywgIASEZYAADJCAsAIJn/B9lK9N9+tiVmAAAAAElFTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "m = B.mean()\n",
        "v = B.var()\n",
        "z = means # (means - m) / np.sqrt(v / N)\n",
        "plt.hist(z, density = True, histtype = \"step\");\n",
        "#x = np.linspace(np.min(z), np.max(z), 101)\n",
        "#Normal = sp.stats.norm()\n",
        "#plt.plot(x, Normal.pdf(x)); # don't need this for Exam 02"
      ],
      "id": "f79c5d65-d8b2-44f1-80ff-4e4fb44c4fe1"
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {},
      "outputs": [],
      "source": [
        "x = B.rvs(size = N)"
      ],
      "id": "8105b6b7-a253-4a71-a465-e63c8ccc75e9"
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90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\nAAAASUVORK5CYII=\n"
          }
        }
      ],
      "source": [
        "ndx = np.arange(1, N + 1)\n",
        "cm = np.cumsum(x) / ndx\n",
        "plt.plot(ndx, cm);"
      ],
      "id": "3da87074-5b61-418e-8c81-5862e0d2ac47"
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "np.float64(7.5)"
            ]
          }
        }
      ],
      "source": [
        "B.mean()"
      ],
      "id": "f986a426-868a-410a-a989-14e65f437ee0"
    }
  ],
  "nbformat": 4,
  "nbformat_minor": 5,
  "metadata": {
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3 (ipykernel)",
      "language": "python"
    },
    "language_info": {
      "name": "python",
      "codemirror_mode": {
        "name": "ipython",
        "version": "3"
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.12.12"
    }
  }
}