Probability Theory

Prerequisite: MATH 202 with a minimum grade of "C-"; and MATH 251 with a minimum grade of "C-" or MATH 261 with a minimum grade of "C-" This calculus-based course provides a foundation for the mathematical theory of statistics. Topics include probability axioms, probability spaces, discrete and continuous random variables and their distributions, joint distributions, transformations of variables, order statistics, expected values, laws of large numbers, the central limit theorem, conditional distributions and their expectations, moment generating functions and characteristic functions. The course also introduces estimation theory, including maximum likelihood estimators, method of moment estimators, the Cramer-Rao lower bound, and sufficiency, efficiency and consistency of estimators, as well as Bayesian estimation. Offered fall and spring semesters.