Welcome to Week 4! This week, we explore probability theory and sampling techniques - essential foundations for statistical inference in agricultural research. Learn to simulate probability experiments, work with distributions, and understand randomness!

🎯 What You'll Learn This Week

🔍 Logical Variables - TRUE/FALSE operations and comparisons

🔄 Data Type Conversion - Transform between different R data types

🎯 Random Sampling - Use sample() function for population sampling

🪙 Coin Toss Simulation - Model probability experiments programmatically

🎲 Dice Roll Simulation - Understand Central Limit Theorem effects

📊 Normal Distributions - Use rnorm(), pnorm(), and qnorm() functions

🚀 Getting Started: Step-by-Step Guide

Step 1: Launch Week 4 Binder Environment 🌐

Click the "Launch Week 4" button above to start your R environment. This will take 2-5 minutes to load with all necessary packages for probability and sampling.

Step 2: Navigate to Class Activity 📚

Once Binder loads, you'll see the Jupyter Notebook interface. In the left panel, you'll see:

assignment/ - Assignment 4 on probability simulation
class_activity/ - Week 4 lab tutorial
Various files (README.md, runtime.txt, etc.)

Click on the class_activity folder to access this week's content.

Step 3: Open the Week 4 Lab Notebook 📖

Inside the class_activity folder, double-click on Week4_Probability_Sampling.ipynb to open the interactive lab notebook.

Step 4: Explore Probability Concepts 🎲

This week we'll work with simulated data and probability distributions! The notebook will guide you through:

Understanding logical variables and data types
Random sampling with and without replacement
Simulating coin tosses and dice rolls
Working with normal distribution functions
Comparing experimental vs theoretical probabilities

🎯 Interactive Learning Tools

Practice with Probability Simulation Tools

Use these interactive tools to understand probability concepts before working with R code:

💡 Tip: Use these tools to visualize probability concepts before applying them in your R notebook!

🧮 Key R Functions This Week

Probability and Sampling

            sample(x, size, replace = TRUE/FALSE)  # Random sampling

            set.seed(number)                       # Reproducible results

            table(data)                            # Frequency counts

            sum(logical_vector)                    # Count TRUE values

            length(data)                           # Total observations

Normal Distribution Functions

            rnorm(n, mean = 0, sd = 1)             # Generate random normal data

            pnorm(q, mean = 0, sd = 1)             # Calculate probabilities

            qnorm(p, mean = 0, sd = 1)             # Find quantiles

            pnormGC(q, mean, sd, graph = TRUE)     # Visual probability (tigerstats)

Data Type Conversion

            as.numeric(x)                          # Convert to numeric

            as.character(x)                        # Convert to character

            as.factor(x)                           # Convert to factor

            as.logical(x)                          # Convert to logical

            data.frame(x)                          # Convert to data frame

📝 Assignment 4: Probability Simulation

Step 1: Access Assignment Folder 📋

From the main directory, click on the assignment folder to access Assignment 4.

Step 2: Open Assignment 4 Notebook 📄

Double-click on Assignment4.ipynb to open your assignment on probability simulation.

Assignment Overview (20 points total)

🎲

Part 1: Simulation (6 points)

Simulate 50 coin flips and 50 dice rolls

📊

Part 2: Probability Calculation (6 points)

Calculate experimental probabilities and compare to theoretical

📈

Part 3: Data Frames and Visualization (8 points)

Create probability distributions and bar plots

Step 3: Simulate Probability Experiments 🎯

The assignment focuses on fundamental probability concepts:

Coin Flip Simulation - Model fair coin tosses and calculate probabilities
Dice Roll Simulation - Generate random dice outcomes and analyze patterns
Experimental vs Theoretical - Compare your results to expected probabilities

Learn to work with discrete probability distributions and understand sampling variability!

🌾 Why This Matters in Agriculture

🌱 Seed Germination Studies - Model probability of germination success

🌧️ Weather Risk Assessment - Simulate drought and frost probabilities

🧪 Quality Control Sampling - Random sampling of agricultural products

🔬 Field Trial Design - Understanding sampling variability

🐛 Pest Management - Model probability distributions of pest occurrence

Probability Skills Help You:

Design experiments with appropriate sample sizes
Understand uncertainty and variability in agricultural systems
Make informed decisions under uncertainty
Calculate risk probabilities for insurance and planning
Interpret statistical test results and confidence intervals

💾 Saving Your Work

⚠️ Important: Binder environments are temporary! Always save your work locally.

Download Your Notebook 📥

When you're done working, save your progress:

Save your notebook: File → Save
Download .ipynb file: File → Download
Export HTML/PDF: File → Save and Export Notebook As → HTML

Continue Your Progress Later 🔄

To resume your work:

Launch Binder again
Click Upload button
Upload your saved .ipynb file
Continue where you left off!

📤 Submission Requirements

For Assignment 4, submit TWO files to UC Davis Canvas:

📄

HTML/PDF Report

Your completed assignment with all outputs and analysis

💾

.ipynb File

Your notebook code as backup

Due Date: Check Canvas for assignment deadline

🎯 Learning Objectives

By the end of this week, you will be able to:

✅ Understand logical variables and data type conversions

✅ Perform random sampling with and without replacement

✅ Simulate probability experiments (coins, dice)

✅ Work with normal distribution functions

✅ Compare experimental and theoretical probabilities

✅ Visualize probability distributions with bar plots

❓ Need Help?

📧 Contact Information

Mohammadreza Narimani
📧 mnarimani@ucdavis.edu
🏫 Department of Biological and Agricultural Engineering, UC Davis

🔧 Common Issues

Binder won't load? Try refreshing or clearing browser cache
Random results different? Use set.seed() for reproducible results
Probability doesn't sum to 1? Check your table() and division calculations
tigerstats error? Make sure the package is loaded with library(tigerstats)

📚 Additional Resources

Probability Theory: Review basic probability rules and concepts
R Documentation: Use ?function_name for help with functions
Practice: Try different sample sizes to see how results change

🌟 Tips for Success

💡 Best Practices

Use set.seed() - For reproducible random results
Start with small samples - Understand concepts before increasing size
Verify your simulations - Check that probabilities sum to 1
Compare to theory - Always relate experimental to expected results
Visualize your data - Plots help understand probability distributions

⚡ Keyboard Shortcuts

Shift + Enter Run current cell and move to next

Ctrl + Enter Run current cell and stay in place

Tab Auto-complete function names

?function Get help for any R function

🎉 Ready to Start?

Click the Binder badge below to launch Week 4!

Launch Week 4 Interactive Environment

Happy probability exploring! 🎲🌾

Last updated: October 2025 | PLS 120 - Applied Statistics in Agriculture | UC Davis
Week 4: Probability and Sampling

🎲 Week 4: Probability and Sampling