Probability spaces and axioms, conditional probability and independence, random variables and vectors, expectation, generating functions, convergence, limit theorems, distribution theory (e.g., relationships among binomial, normal, bivariate normal, chi-square, gamma, beta, t, F, etc.), order statistics, sufficient statistics, consistency, expontial families, method of moments, maximum likelihood estimation, minimum variance unbiased estimation, information inequality, confidence intervals, hypothesis testing, Neyman-Pearson lemma, optimality properties of tests, likelihood ratio tests, Cochran's theorem, basic Bayesian methods.