Theory of Probability and Applications

Jan 1, 2022 — Apr 30, 2022

About the course

This course will cover measure theoretic probability with applications to statistics, including measure theory, measurable functions and random variables, expectation and integration, product spaces, independence, derivatives, conditional probability, characteristic functions, and limit theorems. The material is based on a course that has been taught to students in statistics, mathematics, engineering and science for many years. While rigorous proofs are discussed, the emphasis is on developing an understanding of how measure theory is used as a model for probability theory and how probability theory is used as a physical model. The statistics applications are used to motivate the development. Because it emphasizes foundations, it is paced differently than a common graduate probability theory course, e.g., covers more measure theory, and because it covers probability, it is different than a standard measure theory course.

The plan is to have recorded videos for the longer proofs. Instead of covering proofs in class, I will trim the class time by the length of the videos of proofs of theorems covered in a class and then answer questions about the proofs in the next class. This lets the students go through the proofs at a speed and level of detail that they like but maintains the total time allotted to lectures and still getting to ask questions.

Course work will be based on homework assignments given out every 1.5-2 weeks (so about 7-9 total). I have a resubmission policy in which I let students resubmit selected problems based on feedback received from the first submission.

Registration

This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

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