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Added lesson 13 materials
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‎notebooks/notebooks.yml‎

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file: "Lesson_12_activity.ipynb"
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- name: "Anscombe's quartet demo"
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file: "anscombes_quartet.ipynb"
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- number: "13"
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title: "Probability distributions"
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topics: "Discrete and continuous distributions, central limit theorem"
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notebooks:
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- name: "In class demo"
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file: "Lesson_13_demo.ipynb"
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- name: "Activity"
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file: "Lesson_13_activity.ipynb"

‎notebooks/unit2/lesson_13/Lesson_13_activity.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "b4a46963",
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"metadata": {},
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"source": [
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"# Lesson 13 activity: probability distributions\n",
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"\n",
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"## Learning objectives\n",
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"\n",
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"This activity will help you to:\n",
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"\n",
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"1. Understand and apply binomial distributions to model discrete events\n",
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"2. Demonstrate the Central Limit Theorem through sampling distributions\n",
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"3. Visualize theoretical and empirical probability distributions\n",
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"4. Connect statistical theory to real-world data analysis"
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]
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},
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{
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"cell_type": "markdown",
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"id": "86e3eac2",
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"metadata": {},
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"source": [
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"## Setup\n",
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"\n",
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"Import the required libraries and load the weather dataset."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "117792af",
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"metadata": {},
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"outputs": [],
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"source": [
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"import pandas as pd\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from scipy import stats"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "05634da2",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Load the weather dataset\n",
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"url = 'https://gperdrizet.github.io/FSA_devops/assets/data/unit2/weather.csv'\n",
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"df = pd.read_csv(url)\n",
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"df.head()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "809f038a",
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"metadata": {},
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"source": [
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"## Exercise 1: binomial distribution - modeling rainy days\n",
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"\n",
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"**Objective**: Understand and visualize binomial distributions using real weather data.\n",
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"\n",
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"The binomial distribution models the number of successes in a fixed number of independent trials. In weather forecasting, we can use it to model the probability of rainy days over a period of time.\n",
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"\n",
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"**Tasks**:\n",
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"\n",
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"1. **Calculate the probability of rain**:\n",
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" - Count how many days in the dataset have `rainfall_inches > 0`\n",
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" - Calculate the proportion of rainy days (this is your probability `p`)\n",
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" - Print this probability with an interpretation (e.g., \"Based on our data, there's a X% chance of rain on any given day\")\n",
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"\n",
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"2. **Create a theoretical binomial distribution**:\n",
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" - Assume you're looking at a 30-day period (like a month)\n",
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" - Using the probability from step 1, calculate the theoretical probability of getting exactly k rainy days for k = 0, 1, 2, ..., 30\n",
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" - Use `scipy.stats.binom.pmf()`\n",
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"\n",
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"3. **Visualize the distribution**:\n",
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" - Create a bar plot showing the probability of each possible number of rainy days (0 to 30)\n",
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" - Add a vertical line showing the expected value (mean = n × p)\n",
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" - Label the axes appropriately\n",
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" - Include a title with the probability of rain\n",
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"\n",
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"4. **Interpret** your findings:\n",
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" - What is the most likely number of rainy days in a 30-day period?\n",
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" - What is the expected (mean) number of rainy days?\n",
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" - What's the probability of having 15 or more rainy days in a month?\n",
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" - How does this distribution help weather forecasters make predictions?\n",
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" - **Bonus**: Calculate the standard deviation and explain what it tells you about the variability in monthly rainfall patterns"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "2c5fd71d",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Your code here"
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]
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},
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{
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"cell_type": "markdown",
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"id": "714bd825",
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"metadata": {},
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"source": [
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"## Exercise 2: central limit theorem - sampling distribution of rainfall\n",
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"\n",
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"**Objective**: Demonstrate the Central Limit Theorem by creating and analyzing a sampling distribution.\n",
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"\n",
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"The Central Limit Theorem (CLT) states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's original distribution. This is fundamental to statistical inference.\n",
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"\n",
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"**Tasks**:\n",
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"\n",
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"1. **Examine the population distribution**:\n",
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" - Create a histogram of all `rainfall_inches` values in the dataset\n",
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" - Calculate and print the population mean and standard deviation\n",
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" - Note the shape of this distribution (is it normal, skewed, etc.?)\n",
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"\n",
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"2. **Create a sampling distribution**:\n",
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" - Take 1000 random samples from the rainfall data, each of size n=30\n",
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" - For each sample, calculate the mean rainfall\n",
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" - Store all 1000 sample means in a list or array\n",
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" - Hint: Use `df['rainfall_inches'].sample(n=30, replace=True)` for each sample\n",
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"\n",
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"3. **Visualize the sampling distribution**:\n",
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" - Create a histogram of the 1000 sample means\n",
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" - Overlay a normal distribution curve using the theoretical mean (μ) and standard error (σ/√n)\n",
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" - Add a vertical line at the population mean\n",
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" - You can use `scipy.stats.norm.pdf()` to create the normal curve\n",
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" - Label axes and add a descriptive title\n",
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"\n",
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"4. **Compare distributions**:\n",
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" - Create two side-by-side histograms:\n",
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" - Left: Original rainfall distribution (from step 1)\n",
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" - Right: Sampling distribution of means (from step 3)\n",
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" - Make sure both use the same y-axis scale for comparison\n",
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" - Include the mean and standard deviation in each subplot title\n",
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"\n",
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"5. **Interpret** your findings:\n",
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" - How does the shape of the sampling distribution compare to the original distribution?\n",
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" - Is the sampling distribution approximately normal? (This demonstrates the CLT!)\n",
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" - Calculate the standard error: population σ divided by √30. How does this compare to the standard deviation of your sample means?\n",
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" - What does the CLT tell us about why we can use normal-based methods (like confidence intervals) even when our data isn't normally distributed?\n",
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" - **Bonus**: Repeat the experiment with different sample sizes (n=5, n=10, n=50). How does sample size affect the spread and normality of the sampling distribution?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "a183c001",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Your code here"
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]
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}
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],
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"metadata": {
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"language_info": {
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"name": "python"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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