Theory of Probability (accelerated)

Catalog description

Intensive treatment of probability for graduate and advanced undergraduate students with strong mathematical preparation but no prior background in probability. The course moves quickly through probability axioms, random variables, and expectations, followed by a comprehensive study of named distributions (e.g., hypergeometric, negative binomial, gamma, and beta). Other topics include: conditional expectation, moment generating functions, inequalities, and limit theorems. This course compresses most of the material of Stats 117 and Stats 118 into a single quarter; the pace is accelerated and the workload is heavy (15+ hours per week). Fluency in set theory, Taylor series, multivariable calculus, and linear algebra will be assumed and not reviewed. (For example, it is assumed that most of Chapters 1-3 in https://dlsun.github.io/skis is familiar.) All prerequisites are strictly enforced. Students seeking a standard introduction are strongly encouraged to consider Stats 117 instead. Students with prior background in probability should consider Stats 118 instead, which covers additional content.