diff --git a/Solutions_to_Selected_Problems/SimulationProject.ipynb b/Solutions_to_Selected_Problems/SimulationProject.ipynb new file mode 100644 index 0000000..189b185 --- /dev/null +++ b/Solutions_to_Selected_Problems/SimulationProject.ipynb @@ -0,0 +1,323 @@ +{ + "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": [ + "\"Open" + ] + }, + { + "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": [] + } + ] +} \ No newline at end of file