AP®︎ Statistics (pre-2026) Unit 4: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 4 of AP Statistics (pre-2026) – Probability, Random Variables, and Probability Distributions.
Unit 4: Probability, Random Variables, and Probability Distributions
The rules of probability and how random variables and their distributions set up everything in inference.
Begin with Topic 4.1: Introducing Statistics: R...To review Unit 4, go through each of the 12 topics below.
Everything you actually need to know for your Unit 4 test, pulled directly from the AP® Statistics (pre-2026) curriculum.
Introducing Statistics: Random and Non-Random Patterns?
Introducing Statistics: Random and Non-Random Patterns?
- Random Variation and Non-Random Patterns
- Patterns in Data and the Questions They Suggest
- Why Random Patterns Can Look Non-Random
Estimating Probabilities Using Simulation
Estimating Probabilities Using Simulation
- Random Processes, Outcomes, and Events
- What a Simulation Is and Why It Works
- How to Design and Run a Simulation
Introduction to Probability
Introduction to Probability
- Probability as Long-Run Relative Frequency
- Sample Space and Events
- The Basic Probability Rules
Mutually Exclusive Events
Mutually Exclusive Events
- What the Intersection of Two Events Means
- Mutually Exclusive Events
- The Addition Rule and When to Use It
Conditional Probability
Conditional Probability
- Conditional Probability Explained
- The Multiplication Rule and Joint Probability
- Finding Conditional Probability from Different Representations
Independent Events and Unions of Events
Independent Events and Unions of Events
- What Independent Events Are
- The Multiplication Rule for Independent Events
- What a Union Is
Introduction to Random Variables and Probability Distributions
Introduction to Random Variables and Probability Distributions
- What a Random Variable Is
- Representing a Discrete Probability Distribution
- Finding Probabilities from a Distribution
Mean and Standard Deviation of Random Variables
Mean and Standard Deviation of Random Variables
- Parameters of a Discrete Random Variable
- The Mean or Expected Value \( \mu_X \)
- Variance and Standard Deviation \( \sigma_X \)
Combining Random Variables
Combining Random Variables
- Linear Transformations of a Random Variable
- Linear Combinations of Random Variables
- Means of Sums and Differences
Introduction to the Binomial Distribution
Introduction to the Binomial Distribution
- What a Binomial Random Variable Is
- The Binomial Probability Formula
- Finding Binomial Probabilities
Parameters for a Binomial Distribution
Parameters for a Binomial Distribution
- What a Binomial Random Variable Is
- The Parameters of a Binomial Distribution
- What These Formulas Mean Conceptually
The Geometric Distribution
The Geometric Distribution
- What a Geometric Random Variable Is
- The Geometric Probability Formula
- Mean and Standard Deviation
Notes
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