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Math 170A: General Course Outline

Course Description

170A. Probability Theory. (4)
Lecture, three hours; discussion, one hour. Requisites: courses 32B, 33A, 131A. Not open to students with credit in course 170E, Electrical Engineering 131A or Statistics 100A. Rigorous presentation of probability theory based on real analysis. Probability space, probability and conditional probability, independence, Bayes? rule, discrete and continuous random variables and their distributions, expectation, moments and variance, conditional distribution and expectation, weak law of large numbers. P/NP or letter grading.

Course Information:

The course discusses the foundations of probability as a mathematical discipline rooted in undergraduate real analysis. At the end of the course, the students will have the tools and ability to formulate, analyze an answer questions in probability and prove the validity of their reasoning in full mathematical rigor.

Textbook(s)

Probability: An Introduction (2nd ed.). by Grimmett, G. R., & Welsh, D. J. (2014).Oxford: Oxford University Press.

Outline update: T. Austin, 01/20

Schedule of Lectures

Lecture Section Topics

Week 1

Sections 1.1-1.5, 1.9

Sample space, events, probability

Week 2

Sections 1.6-1.7

Conditional probability and independence

Week 3

Sections 1.8, 1.10

Partition theorem and Bayes rule, examples

Week 4

Sections 2.1-2.4

Discrete random variables, their functions, expectation and variance

Week 5

Sections 2.5, 3.1-3.2

Conditional expectation, multivariate discrete distributions

Week 6

Sections 3.3-3.5

Independent discrete random variables, indicators

Week 7

Sections 5.1-5.6

Cumulative distribution function, continuous random variables

Week 8

Sections 6.1-6.4

Multivariate distributions and their marginals

Week 9

Sections 6.5-6.7

Change of variables, conditional expectation

Week 10

Sections 6.8, 7.3, 8.1-8.2

Mutlivariate normal distribution, weak law of large numbers