Ross's "A first course in probability"

Syllabus

Chapter 1, pp 13—33.

Combinatorial analysis. Counting, permutations, combinations, multinomial coefficients, counting solutions.
Chapter 2

Axioms of probability. Sample space and events, axioms, sample spaces, equally likely outcomes, continuous set functions, measures of belief
Chapter 3

Conditional probability and independence. Bayes's formula, independent events, \(P(\cdot|F)\).
Chapter 4 (exclude 4.8.4)

Discrete random variables. Expectation values for functions; variance. Bernoulli, binomial, Poisson, and other random variables (exclude Zipf). Expected sums, properties of cdfs.
Chapter 5 (exclude 5.6.2, 5.6.3, 5.6.5, 5.7)

Continuous random variables. Expectation and variance. Uniform, normal, exponential, gamma, beta. Skip gamma, Weibull, and Pareto distributions; skip the distribution of functions of random variables.
Chapter 6, sections 6.1, 6.2, 6.3.3, 6.3.4, 6.4, 6.6

Jointly-distributed random variables. Independent random variables and their sums (but only for normally distributed variables); conditional distributions. Several skipped topics.
Chapter 7, Discrete only: exclude 7.2.1, 7.2.2, 7.3, 7.6, 7.7, 7.8, 7.9

Properties of expectations. Covariance and correlations; conditional expectation. Most of the chapter is skipped.
Chapter 8, sections 8.1, 8.3

Limit theorems, but just the Central Limit theorem.