Fall 2017

TR 11:00--12:15 SNOW 301

Terry Soo, Snow 610

Office hours: Tuesdays 4-5. Wednesday 2.30-3.50.

Course description.

This is a pre-measure theoretic introduction to probability theory. We do not assume any knowledge of measure-theory, but we will develop necessary background as needed. Highlights will include the law of large numbers and the central limit theorem.

Prerequisites.

Undergraduate degree in mathematics. This is a graduate course. Proofs will be an important part of the course. Students should be comfortable with reading and writing proofs.

This course will help students who are preparing for the Probability and Statistics qualifying examination, and requires a high level of mathematical maturity.

Grading

Subject to revision

Homework: 20%

Midterm 1: 20% September 21. M1Q M1S

Midterm 2: 20% November 2. M2S

Final examination 40% December 12. 10.30-1 PM. Registrar Final exam schedule

Final Exam

Textbook and lecture notes:

No textbook is required. I will post lecture notes online.

Other suitable references are:

Probability and random processes. Grimmett and Stirzaker

Knowing the odds: An introduction to the probability. John Walsh

Probability. Karr

Statistical inference. Casella and Berger

More advanced:

Probability: Theory and examples. Durrett

Foundations of modern probability. Kallenberg

Real analysis and probability. Dudley

Notes:

Probability Spaces

Uncountable probability spaces

Counting

Conditional probability

Random variables I

Random variables II

Expectation I

Expectation II

Variance

Convergence of RV I

Convergence of RV II

Characteristic functions

Some problems of a computational nature

Cauchy-Schwarz and Jensen's inequalties

Conditional distributions and expectations

Homework--to be submitted at the beginning of class

HW1: Due Tuesday September 5. HW1 solutions

HW2: Due Tuesday September 12. HW2 solutions

HW3: Due Tuesday September 19. HW3 solutions

HW4: Due Thursday October 5. HW4 solutions

HW5: Due Thursday October 12 HW5 partial sol

HW6: Due Thursday October 26 HW6 sol

HW7: Due Thursday November 16 HW7 partial sol

HW8: Due Thursday November 30 HW8 sol