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

## Instructors

Feng Ruan

## Meeting Info

University Library 4670: 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 theoryâ€”the law of large numbers and the central limit theorem.

## 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Title: Probability Theory Unpublished Lecture Notes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/