810—Probability Theory I. [=MATH 710] (3 credit hours) (Prerequisites: STAT 511, 512, or MATH 703) Probability spaces, random variables and distributions, expectations, characteristic functions, laws of large numbers, and the central limit theorem.

Course Homepage: Recent Semester

Usually Offered: Fall Semesters, Even years

Purpose: To acquaint advanced graduate students in statistics and other disciplines with the theoretical and abstract foundations of probability. To provide a foundation for further study in probability theory, stochastic processes, and statistical theory at the doctoral level.

Current Textbook: Resnick, S. I. (2014).  A Probability Path. New York, NY: Springer. 

Topics Covered	Chapters	Approx. Time
Sets, Classes of Sets, Events Probability Spaces, Random Variables, Induced Probability Measures, Extension Theorems	1-3	5.5 weeks
Independence, Expectation, Conditional Expectation and Probability, Product Spaces and Measures	4-5, 10.1-10.3	5.5 weeks
Basic Convergence Concepts (in distribution, in probability, almost sure, in Lp-mean, uniform integrability)	6	3 weeks

The above textbook and course outline should correspond to the most recent offering of the course by the Statistics Department. Please check the current course homepage or with the instructor for the course regulations, expectations, and operating procedures.  

Contact Faculty: Edsel Peña, Dewei Wang