Probability and Statistics I

ECON 509 is the measure-theoretic foundation that turns "statistics" from a toolbox into something you can actually prove things about — you build random variables and their distributions from scratch, then push them through convergence theorems until estimation and testing fall out as consequences rather than recipes. Expect dense weekly problem sets out of Casella & Berger, ten quizzes that force you to keep up with the derivations, and exams that ask you to construct arguments (MLE asymptotics, UMP tests, LM/Wald) rather than plug into formulas. It's the gateway course for the entire econometrics sequence — every identification, efficiency, and inference claim you'll make later in ECON 510 and beyond traces back to the limit theorems and likelihood theory you internalize here.