{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#"
      ],
      "id": "e0e6cd28-15cb-4ce3-bf2e-45ab352f9286"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy as sp"
      ],
      "id": "13084158-35da-4172-9dce-0a1f1fdb4d0b"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "# 1\n",
        "m = 50_000\n",
        "s = 2_000\n",
        "X = sp.stats.norm(loc = m, scale = s)"
      ],
      "id": "df4a9539-b52d-4225-b79c-5549353eccb6"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.15865525393145707"
            ]
          }
        }
      ],
      "source": [
        "# 1a\n",
        "X.cdf(48_000)"
      ],
      "id": "9f5079f7-d986-42ae-8c26-cd60c44f1ea0"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "52563.1031310892"
            ]
          }
        }
      ],
      "source": [
        "X.ppf(.9)"
      ],
      "id": "9eab9dab-30f7-467f-83ae-189b64551035"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "3.056696706382561e-138"
            ]
          }
        }
      ],
      "source": [
        "# made up question\n",
        "# How much probability does \n",
        "# this distribution put over negative numbers?\n",
        "X.cdf(0)"
      ],
      "id": "15008e02-aac7-4f69-a756-4f63a06439f6"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.9999366575163338"
            ]
          }
        }
      ],
      "source": [
        "# How much probability lives between \n",
        "# 4 sigma of mu?\n",
        "X.cdf(m + 4 * s) - X.cdf(m - 4 * s)\n"
      ],
      "id": "8f75ea5b-7cdc-476e-98c2-c39ad900daba"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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Js2fPVm5urkpLSyVJM2fO1NKlS3X55ZersLBQe/bs0aJFizRz5syOUILweL59iuYrkxkV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\n"
          }
        }
      ],
      "source": [
        "ss = np.linspace(0, 10, 100)\n",
        "p = X.cdf(m + ss * s) - X.cdf(m - ss * s)\n",
        "plt.plot(ss, p);"
      ],
      "id": "e4012300-3295-4daf-bcd0-e50f2d79febe"
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [],
      "source": [
        "# 1\n",
        "X = sp.stats.norm(loc = 10, scale = 2)"
      ],
      "id": "b40089f9-2284-432a-828f-09f5e295baa8"
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.6826894921370859"
            ]
          }
        }
      ],
      "source": [
        "# 1a\n",
        "X.cdf(12) - X.cdf(8)"
      ],
      "id": "2ff5efe5-ad91-430b-a222-9a5533ec12b3"
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.02275013194817921"
            ]
          }
        }
      ],
      "source": [
        "1 - X.cdf(14)"
      ],
      "id": "813fa2d1-4752-4c55-8985-18bf607b106b"
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [],
      "source": [
        "#3\n",
        "X = sp.stats.norm(loc = 5.2, scale = 0.8)"
      ],
      "id": "3b14bafe-7d31-4aea-98c4-c02044facc43"
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.06680720126885806"
            ]
          }
        }
      ],
      "source": [
        "#3a\n",
        "X.cdf(4)"
      ],
      "id": "fcf1ba20-6efe-4596-8663-a4e1ecd3ca9d"
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.15865525393145707"
            ]
          }
        }
      ],
      "source": [
        "# 3b\n",
        "1 - X.cdf(6)"
      ],
      "id": "09fdac0b-c778-438c-9373-adc58566cfc3"
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "6.225241252435681"
            ]
          }
        }
      ],
      "source": [
        "X.ppf(.9)"
      ],
      "id": "8e9c5c33-ac94-4388-ad49-d7ad02e5af77"
    }
  ],
  "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"
    }
  }
}