Lecture, three hours; discussion, one hour. Requisites: courses 32B, 33A, 131A. Not open to students with credit for course 170E, Electrical and Computer 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.