MATH 149A: Probability and Mathematical Statistics
Summer 2025

Instructor: Boris Tsvelikhovskiy    borist AT ucr.edu

Overview

This course introduces the fundamental concepts of probability, starting with probability distributions on finite sets and basic counting principles. We explore conditional probability, Bayes’ formula, and independence, then move to random variables - both discrete and continuous - including their probability distributions, cumulative distributions, expectations, variances, and standard deviations. Key tools such as Markov’s and Chebyshev’s inequalities are developed to bound probabilities of deviations from the mean. The course concludes with joint, marginal, and conditional distributions of two random variables, the distribution of sums of independent variables via convolution, and applications to problems involving multiple random quantities.

Textbook

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Lecture notes

Homework problems

Review and Practice Materials