Probability Theory

STAT7032, Spring semester, 2015

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall
Office Hours: W 1:30-3:15pm, or by appointment.
Class meeting: M W F 12:20pm - 01:25pm, 4206 French Hall (Seminar Room)

Textbook

Probability: Theory and Examples, 4th Edition (Cambridge Series in Statistical and Probabilistic Mathematics) by Rick Durrett.
A PDF version from the website of the author.

Course description

We will cover the following materials: measure-theoretic foundations of probability; laws of large numbers; central limit theorems; weak convergence; characteristic functions.

Chapters 1-3 from the textbook will be covered.

Pre-req: A good knowledge of multivariable calculus and an introduction to analysis is a must. Students are expected to have a strong background in mathematics or theoretical statistics. Advanced Calculus (MATH 6001/6002), Mathematical Statistics (STAT 6021/6022), or equivalent are recommended.

Grades

• Grading: homework 30%, midterm 30%, final 30%, participation 10%

Tentative Schedule and Homework

• Week 1 (01/11-01/17): Chapter 1.1. HW1 (due Jan 26)
• Week 2 (01/18-01/24, MLK): Chapter 1.1.
• Week 3 (01/25-01/31): Chapter 1.2, 1.3. HW2 (due Feb 2)
• Week 4 (02/01-02/07): Chapter 1.4, 1.5. HW3 (due Feb 13)
• Week 5 (02/08-02/14): Chapter 1.6. No class Feb 9. HW4 (due Feb 23 Monday)
• Week 6 (02/15-02/21): Chapter 1.6, 1.7.
• Week 7 (02/22-02/28): Chapter 2.1. HW5 (due March 2 Monday)
• Week 8 (03/01-03/07): Chapter 2.1, 2.2. HW6 (due March 11 Wednesday)
• Week 9 (03/08-03/14): Chapter 2.3, 2.4. HW7 (due March 23 Monday)
• Week 10 (03/15-03/21): Spring Break.
• Week 11 (03/22-03/28): Chapter 2.5. Midterm, Fri March 27, 12:20pm - 1:20pm. HW8 (due April 1 Wednesday)
• Week 12 (03/29-04/04): Chapter 3.1, 3.2.
• Week 13 (04/05-04/11): Chapter 3.3, 3.4. HW9 (due April 20 Monday)
• Week 14 (04/12-04/18): No class this week.
• Week 15 (04/19-04/25): Review. Review Sheet
• Week 16 (04/26-05/01): Final, Tues April 28, noon - 2pm, in classroom.

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