Probability for Statistical Inference 1 (430-1-20)

Instructors

Feng Ruan

Meeting Info

Parkes Hall 212: Tues, Thurs 2:00PM - 3:20PM

Overview of class

This is a course on foundations of (measure theoretic) probability theory. The course introduces foundational concepts in measure theoretic probability including probability spaces, random variables, integrations and expectations, product measures and independence, and covers topics including (weak/strong) law of large numbers, and central limit theorems and their variants (e.g., local central limit theorem).

Registration Requirements

Math 320-1 (Real Analysis) and Statistics 420-1 (Introduction to Statistical Theory and Methodology 1) or equivalent.

Learning Objectives

The students are expected to grasp the foundational concepts of measure theoretic probability theory, and understand the two major results of probability theory—the law of large numbers and the central limit theorem.

Teaching Method

Lectures

Evaluation Method

Homework 40%, Midterm Exam 30%, Final Exam 30%

Class Materials (Required)

Main Textbook
Title: Probability: Theory and Examples
Author: Rick Durrett
Edition: 5th Edition
ISBN-13: 978-1108473682

Class Materials (Suggested)

(i)
Title: Probability and Measure
Author: Patrick Billingsley
Edition: Anniversary Edition
ISBN-13: 978-1118122372

(ii)
Title: Probability Theory Unpublished Lecture Notes
Author: Terence Tao
Available Online: https://terrytao.wordpress.com/category/teaching/275a-probability-theory/