- Chapter 1, Lab 1: Spaces, events, basic counting, exponential approximation
- Chapter 2: Addition and multiplication rules; conditioning and updating
- Chapter 5: Unions and intersections of several events
- Section 9.1: Probabilities by conditioning and recursion (discrete)
- Section 20.2: Probabilities by conditioning on a continuous variable
- Sections 4.5, 20.3: Independence

- Chapter 3: Intro; equality versus equality in distribution
- Chapter 4: Joint, marginals, conditionals, independence (discrete case)
- Sections 5.3, 5.4: Random permutations and symmetry
- Sections 15.1, 15.2: Density
- Section 15.1 and Lab 7: CDF and inverse CDF
- Chapter 16, Lab 8: Density of a transformation
- Chapter 17, Lab 8: Joint, marginal, and conditional densities; independence
- Chapters 14, 19: Distribution of sum
- Section 14.3, 14.4, 15.3, 19.3: Central Limit Theorem

- Chapter 8: The crucial properties (discrete case) including method of indicators and expectations of functions
- Lab 3: Tail sum formula and applications; see also geometric distribution
- Section 12.3, 19.4: Bounds: Markov, Chebyshev, Chernoff
- Section 9.2, 9.3: Expectation by conditioning
- Section 15.3, 17.1: Expectation using densities and joint densities
- Section 14.1, 14.2, 21.2: Generating functions

- Chapter 12: Intro, linear transformations
- Chapter 13: Covariance; variance of a sum
- Lab 6: Application of mean and variance of simple random sample sum
- Homework 11: Correlation and its properties
- Sections 22.2, 22.3: Variance by conditioning, mixtures
- Sections 23.1, 25.1: Mean and covariance for random vectors

- Section 8.2: Unbiased estimates
- Sections 14.4, 14.5: IID sample mean; confidence interval for population mean
- Section 20.1: Maximum likelihood estimate
- Section 20.2: Posterior density, MAP estimate
- Sections 12.2, 22.1, 22.4: Expectation and conditional expectation as least squares predictors
- Sections 24.2, 25.2: Least squares linear predictor

- Sections 8.1, 12.1: Uniform on 1, 2, …, n
- Sections 6.1, 6.2, Chapter 7, 13.2, 14.3, Chapter 21: Bernoulli, binomial and multinomial
- Sections 6.3, 8.2, 13.3, 13.4, Lab 2: Hypergeometric
- Section 6.4, 6.5, Chapter 7, Sections 8.1, 8.3, 12.1, 19.2 and related homework, Lab 9: Poisson
- Homework 3, Lab 4, Lab 9, Sections 9.3, 22.3: Geometric

- Section 15.3, 19.1: Density, expectation, variance, CDF, density of sum

- Section 17.4: Integer parameters; uniform order statistics
- Chapter 21: Relation with binomial; beta-binomial distribution

- Section 14.3: CLT
- Sections 14.4, 14.5: Normal confidence intervals
- Section 16.1: Normal densities
- Sections 18.1, 18.2, 18.4: Independent normal variables, linear combinations, squares, Rayleigh, chi squared
- Section 19.3: Normal MGF, sums, CLT
- Chapter 24, Lab 11: Bivariate normal, linear combinations, independence, regression
- Chapters 23, 25: Multivariate normal, linear combinations, independence, regression

- Section 15.4: Exponential
- Homework 8: Gamma function, gamma density, mean, variance
- Sections 18.3, 18.4: Gamma and chi squared
- Sections 19.2: Sums of independent gammas with the same rate
- Lab 9: Waiting times in a Poisson process

- Chapters 10, 11
- Section 12.4
- Section 25.1, 25.2