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nurfnick · Nov 8, 2023 · 477a78e · 477a78e
1 parent 9bee4f6
commit 477a78e
Showing 1 changed file with 323 additions and 0 deletions.
diff --git a/Solutions_to_Selected_Problems/SimulationProject.ipynb b/Solutions_to_Selected_Problems/SimulationProject.ipynb
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+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "provenance": [],
+      "authorship_tag": "ABX9TyPYIF8u/qzvbHCNXsh/jbI+",
+      "include_colab_link": true
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    },
+    "language_info": {
+      "name": "python"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "<a href=\"https://colab.research.google.com/github/nurfnick/Operations_Research/blob/main/Solutions_to_Selected_Problems/SimulationProject.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# Solutions to Simulation Project"
+      ],
+      "metadata": {
+        "id": "DyS8R-7sNWVp"
+      }
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 2,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "zVyGjZFHNVc9",
+        "outputId": "fb6c7b91-4169-43cc-d93f-e47ad5fe6868"
+      },
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "10"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 2
+        }
+      ],
+      "source": [
+        "import random\n",
+        "\n",
+        "random.choices([10,9],[9,1])[0]"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Let's do it a bunch"
+      ],
+      "metadata": {
+        "id": "wpyL5dEWNr5X"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "cho = []\n",
+        "\n",
+        "for i in range(1000):\n",
+        "  cho.append(random.choices([10,9],[9,1])[0])"
+      ],
+      "metadata": {
+        "id": "KkAVPYezNmfp"
+      },
+      "execution_count": 3,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "sum(cho)/len(cho)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "1TqqGqUqN47q",
+        "outputId": "88dd91cb-810d-4840-9ebb-a49ec4b809df"
+      },
+      "execution_count": 5,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "9.896"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 5
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "I meant for you to use a simple binomial approach.  With success being $\\frac1{10}$ Let's see how I might simulate that."
+      ],
+      "metadata": {
+        "id": "KFVNovugO44i"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "random.choices([1,0],[1,9])[0]"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "NI3aPmz6N8BL",
+        "outputId": "42cf7ff0-c7c6-4c09-acca-b925f9cb8536"
+      },
+      "execution_count": 7,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "0"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 7
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "numtests = []\n",
+        "for i in range(1000):\n",
+        "  test = []\n",
+        "  while sum(test) ==0:\n",
+        "    test.append(random.choices([1,0],[1,9])[0])\n",
+        "  numtests.append(len(test))"
+      ],
+      "metadata": {
+        "id": "MRHYESViPPoc"
+      },
+      "execution_count": 10,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "sum(numtests)/len(numtests)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "TyZ3OysGPqI5",
+        "outputId": "d825151f-1589-40ac-e563-2baf78705eb3"
+      },
+      "execution_count": 12,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "9.975"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 12
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "test.index(1)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "2c-6OXUTP05n",
+        "outputId": "1d8c5601-8329-4408-d0b8-b05f071abc99"
+      },
+      "execution_count": 17,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "9"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 17
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "rs = [10,10,10,10,10,10,10,10,10,9]\n",
+        "random.shuffle(rs)\n",
+        "rs"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "d2VTdmw0QvNB",
+        "outputId": "5493503e-d241-40e4-c6da-e33eb9df24c9"
+      },
+      "execution_count": 27,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "[10, 9, 10, 10, 10, 10, 10, 10, 10, 10]"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 27
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "rs.index(9)+1"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "vl0LHOyZQ5BP",
+        "outputId": "3d44dbc3-584a-4c6f-c99d-fdf304b0e3a4"
+      },
+      "execution_count": 30,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "2"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 30
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "pos = []\n",
+        "\n",
+        "for i in range(1000):\n",
+        "  random.shuffle(rs)\n",
+        "  pos.append(rs.index(9)+1)"
+      ],
+      "metadata": {
+        "id": "Sotpea4JQ_oI"
+      },
+      "execution_count": 34,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "sum(pos)/len(pos)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "9_NNlvcvRjGY",
+        "outputId": "7a794b4e-d006-4f8d-e96b-d4273df27e33"
+      },
+      "execution_count": 35,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "5.379"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 35
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [],
+      "metadata": {
+        "id": "r3vvsxphRlYO"
+      },
+      "execution_count": null,
+      "outputs": []
+    }
+  ]
+}