{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Probability (as a limit point)"
      ],
      "id": "5b17f10c-46af-4ee4-8c5a-204c04dd178c"
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "id": "d769c07c-fa0b-4b8c-8dab-7ec2df6fa865"
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {},
      "outputs": [],
      "source": [
        "def uniform_density(x, a = 1, b = 6):\n",
        "    xa = x < a\n",
        "    xb = x > b\n",
        "    idx = xa | xb\n",
        "    d = np.zeros_like(x)\n",
        "    d[~idx] = 1 / (b - a + 1)\n",
        "    return d"
      ],
      "id": "487eaaa9-27b3-47c2-9e5e-1ed7a40c5833"
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "array([0.16666667, 0.16666667, 0.16666667, 0.        ])"
            ]
          }
        }
      ],
      "source": [
        "x = np.array([1., 3, 6, 10]) # still doesn't work, but I know why\n",
        "uniform_density(x)"
      ],
      "id": "c9988c4a-a1fe-4c15-8d55-21df1bc27ece"
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "(array([False, False, False, False]), array([False, False, False,  True]))"
            ]
          }
        }
      ],
      "source": [
        "x1 = x < 1 \n",
        "x6 = x > 6\n",
        "x1, x6"
      ],
      "id": "0673a82d-7fdf-4e78-adef-a242a59db723"
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "array([ True,  True,  True, False])"
            ]
          }
        }
      ],
      "source": [
        "idx = x1 | x6\n",
        "~idx"
      ],
      "id": "869fecc4-848b-4e95-9276-99b81768f179"
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "array([0, 1, 2])"
            ]
          }
        }
      ],
      "source": [
        "np.arange(np.size(x))[~idx]"
      ],
      "id": "0804eabf-f748-444f-acb1-119de15fe864"
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "array([ 1.,  3.,  6., 10.])"
            ]
          }
        }
      ],
      "source": [
        "x"
      ],
      "id": "e00222ef-4b5f-47e6-9351-2a50f5bdb786"
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "array([1., 1., 1., 1.])"
            ]
          }
        }
      ],
      "source": [
        "np.ones_like(x)"
      ],
      "id": "40d4e17d-2fcd-4ad3-acc8-96659e77f6ee"
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "array([0., 0., 0., 0.])"
            ]
          }
        }
      ],
      "source": [
        "np.zeros_like(x)"
      ],
      "id": "7dde4eed-dd53-4ff3-a5ab-01414f44c622"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "$$\\lim_{N \\rightarrow \\infty} \\frac{1}{N} \\sum_{n=1}^N 1_A(x_n) = \\mathbb{P}[X \\in A]$$"
      ],
      "id": "f4ea9c89-12d9-45e5-8c49-71ab8891f1da"
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {},
      "outputs": [],
      "source": [
        "rng = np.random.default_rng()\n",
        "N = 1000\n",
        "x = rng.integers(1, 7, size = N) # Uniform(1, 6)"
      ],
      "id": "019eead7-f8aa-4de5-b687-3f0a79ed330a"
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.164"
            ]
          }
        }
      ],
      "source": [
        "np.mean(x == 6)"
      ],
      "id": "08e2cee2-daf5-4b84-8ec4-9e4825761e3d"
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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cpKSktLyAXI6UlBRkZWV1etzzzz+P0NBQPPTQQ916H4vFArPZ7PLoC13VPr47XYqXvznV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\nAABJRU5ErkJggg==\n"
          }
        }
      ],
      "source": [
        "ndx = np.arange(1, N + 1)\n",
        "cm = np.cumsum(x == 6) / ndx # mean of data == 6\n",
        "plt.plot(ndx, cm);"
      ],
      "id": "bb14131f-d17d-4953-9fce-b047314ec7ec"
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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M4fNhhJYRAADMRRhhzAgAAKby+TBirbgCtIwAAGAOnw8jzpYR0ggAAKYgjLBRHgAApiKM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\nuavTqo5Fur8q6t8nDNQDH23W/SO7un0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          }
        }
      ],
      "source": [
        "ndx = np.arange(1, N + 1)\n",
        "m = (6 + 1) / 2 # mean of distribution\n",
        "v = ((6 - 1 + 1) ** 2 - 1) / 12 # variance of distribution\n",
        "cm = np.cumsum((x - m) ** 2) / ndx # variance of data\n",
        "plt.plot(ndx, cm);\n",
        "plt.axhline(v, color = \"black\");"
      ],
      "id": "fac025ae-7732-48ff-929b-b05b97de5102"
    }
  ],
  "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"
    }
  }
}