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

**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****Central Limit Theorem****Law of Large Numbers**