{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#"
      ],
      "id": "ba249d2e-515d-4167-9633-af287a611623"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy as sp"
      ],
      "id": "4644ed36-42be-43e5-887c-ede6f760f5b0"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Examples from [webpage](https://roualdes.us/lecturenotes/exponential)"
      ],
      "id": "666532e1-04fd-411c-b10c-c2cb453d1db6"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "# 1\n",
        "X = sp.stats.expon(scale = 5000)"
      ],
      "id": "c6474944-8573-4575-9cf1-d6f9b11db134"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.3934693402873666"
            ]
          }
        }
      ],
      "source": [
        "# 1a\n",
        "X.cdf(2500)"
      ],
      "id": "35a2fa44-323b-4a90-a680-b481dc5f04d2"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.3011942119122022"
            ]
          }
        }
      ],
      "source": [
        "# 1b\n",
        "1 - X.cdf(6000)"
      ],
      "id": "01b3c443-19b4-4113-9bd5-4055ea38721d"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [],
      "source": [
        "#2\n",
        "X = sp.stats.expon(scale = 5000)"
      ],
      "id": "a3f321bc-e0a7-4bff-a8f9-631525b204d5"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.24659696394160646"
            ]
          }
        }
      ],
      "source": [
        "# 2a\n",
        "1 - X.cdf(7000)"
      ],
      "id": "198efb53-a935-4d20-9d6a-3cc2f942d386"
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [],
      "source": [
        "# 2b\n",
        "t = X.ppf(0.1)"
      ],
      "id": "0f86423e-8ba9-43cc-9623-6092d7f84edf"
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.10000000000000002"
            ]
          }
        }
      ],
      "source": [
        "X.cdf(t)"
      ],
      "id": "5af84f87-2e6c-46b8-ace4-ba65bb1e4ae4"
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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AwEYiV1ZJzMkBAAA2EorqyWG4CgAA2ETwuJ6cRAchBwAA2ERkuMqZ6FBCAiEHAADYRGM3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\n/wcfLb2h9dU8LgAAAABJRU5ErkJggg==\n"
          }
        }
      ],
      "source": [
        "# can we plot the ppf function?\n",
        "p = np.linspace(1e-5, 1 - 1e-5, 100)\n",
        "plt.plot(p, X.ppf(p));"
      ],
      "id": "686e0277-f8fe-4057-a133-6841e5b6fe03"
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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XZw7TN7jMOwCgmwgj8FtDs0d3/39FOlXbpMnpCfqfL09iCS8AoNsII/Dbo699pO1HqpQU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\ngg==\n"
          }
        }
      ],
      "source": [
        "# can we plot the CDF?\n",
        "x = np.linspace(1e-5, 50000, 100)\n",
        "plt.plot(x, X.cdf(x));"
      ],
      "id": "5baa5410-5912-4f96-9878-f36d11e5db61"
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "11512.925464970229"
            ]
          }
        }
      ],
      "source": [
        "# How long will it take for the \n",
        "# longest lasting 10% of capacitors\n",
        "# to fail?\n",
        "X.ppf(.9)"
      ],
      "id": "a5ee1d5e-24ee-4532-9670-8c5e5db531d5"
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.36912583412343714"
            ]
          }
        }
      ],
      "source": [
        "# What is the probability that a \n",
        "# capacitor will last between 2000 and\n",
        "# 6000 hours?\n",
        "X.cdf(6000) - X.cdf(2000)"
      ],
      "id": "94a9d1c4-8fe3-4526-b3c2-8b2756300eec"
    }
  ],
  "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"
    }
  }
}