Math

Permutations, combinations, multinomials, stars and bars, inclusion-exclusion, and pigeonhole.

Sample spaces, conditional probability, Bayes' rule, and the law of total probability.

Linearity of expectation, indicators, LOTUS, conditional expectation, and tail sums.

Named distributions (Bernoulli/binomial, geometric, Poisson, uniform, normal, exponential/gamma), order statistics, and their properties.

Variance, covariance, estimators (MLE/Fisher information), regression, hypothesis testing, CLT/LLN, and concentration inequalities.

Markov chains, random walks, recurrence relations, martingales, and gambler-ruin/first-passage reasoning over evolving processes.