{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(lec7_live_complete)=\n",
"# [complete] Lecture 7 live coding\n",
"\n",
"**2025-02-25**\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Law of Total Expectation"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import ipywidgets as widgets"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Set random seed for reproducibility\n",
"rng = np.random.RandomState(42)\n",
"n_samples = 10000"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Suppose we're looking at average coffee prices globally over two types of coffee beans: Arabica and Robusta.\n",
"\n",
"$$\n",
"X = \\begin{cases}\n",
"1 & \\text{if coffee is Arabica} \\\\\n",
"0 & \\text{if coffee is Robusta}\n",
"\\end{cases}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1, 0, 1, 1, 1])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# # generate a random variable X with 80% arabica and 20% robusta\n",
"X = rng.choice([0, 1], size=n_samples, p=[0.2, 0.8])"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# COMPLETED CELL\n",
"# # generate a random variable X with 80% arabica and 20% robusta\n",
"# X = rng.choice([1, 0], size=n_samples, p=[0.8, 0.2])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let $Y$ be the price of coffee in dollars per pound.\n",
"\n",
"Arabica prices are higher, on average:\n",
"$$\n",
"Y \\sim \\begin{cases}\n",
"\\mathcal{N}(4.5, \\;0.75^2) & \\text{if coffee is Arabica} \\\\\n",
"\\mathcal{N}(2.0, \\;0.25^2) & \\text{if coffee is Robusta}\n",
"\\end{cases}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" is_arabica | \n",
" price $/lb | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 1 | \n",
" 3.517227 | \n",
"
\n",
" \n",
" | 1 | \n",
" 0 | \n",
" 2.048971 | \n",
"
\n",
" \n",
" | 2 | \n",
" 1 | \n",
" 4.078259 | \n",
"
\n",
" \n",
" | 3 | \n",
" 1 | \n",
" 4.295241 | \n",
"
\n",
" \n",
" | 4 | \n",
" 1 | \n",
" 5.240613 | \n",
"
\n",
" \n",
"
\n",
"