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
