This is an attempt. Things may change as we go. The numbers represents the section and subsection of the textbook:

## A First Course in Probability

by Sheldon Ross

### 1. Combinatorial Analysis

- Principle of Counting
- Permutations
- Combinations
- Number of Integer Solutions of Equations

### 2. Axioms of Probability

- Sample Space and Events
- Axioms of Probability
- Some Simple Propositions
- Sample Spaces Having Equally Likely Outcomes
- Probability as a Continuous Set Function
- Probability as a Measure of Belief

### 3. Conditional Probability and Independence

- Conditional Probabilities
- Bayes’s Formula
- Independent Events
- P(.|F) is a Probability

### 4. Random Variables

- Random Variables
- Discrete Random Variables
- Expected Value
- Expectation of a function of a RV
- Variance
- Bernoulli and Binomial
- Poisson RV
- Geometric RV
- Expected Value of Sums of Random Variables
- Properties of the Cumulative Distribution Function

### 5. Continuous Random Variables

- Expectation and Variance of Continuous RV
- Uniform RV
- Normal RV
- Exponential RV
- Distribution of a Function of a RV

### 6. Jointly Distributed Random Variables

- Joint Distribution Functions
- Independent RV
- Sum of Independent RV: Examples

### 7. Properties of Expectation

- Expectation of Sums of Random Variables
- Moments of the Number of Events that Occur
- Covariance, Variance of Sums and Correlations
- Conditional Expectation
- Conditional Expectation and Prediction
- Moment Generating Function

### 8. Limit Theorems

- Chebyshev’s Inequality and Weak Law of Large Numbers
- CLT
- LLN