Probability Theory for Statistical Inference

Continuation of STATS 117, with a focus on probability topics useful for statistical inference. Sampling distributions of sums, means, variances, and order statistics of random variables. Convolutions, moment generating functions, and limit theorems. Probability distributions useful in statistics (gamma, beta, chi-square, t, multivariate normal). Applications to estimation and hypothesis testing. Prerequisites: Math 51, MATH 52 (may be taken concurrently), and STATS 117, or equivalent courses. See https://statistics.stanford.edu/course-equiv for equivalent courses in other departments that satisfy these prerequisites.