Introduction to Probability — Bertsekas & Tsitsiklis

Dimitri P. Bertsekas & John N. Tsitsiklis, 2nd Edition

Systematic development of probability theory: sample spaces, random variables, expectation, variance, conditional probability, Bayes rule, limit theorems, and the basic stochastic processes (Bernoulli/Poisson processes and Markov chains). Deeper reading behind Course 1 Parts III–IV.

Chapters

Exercises added as I work through each chapter.