This is a rigorous introductory text in probability and statistics that also develops, in a rigorous fashion, all the necessary supporting mathematics beyond calculus and linear algebra. The mathematics are explained clearly and with full precision in the appendices and supplementary modules, which is a novel approach. Several examples, most of which deal with real problems in computer science (CS) and engineering, compensate for the perceived coldness of the “theorem: proof” prose. Instead of placing balls in urns and using dice to present basic examples, it uses very basic topics from CS to exemplify the theory in such a way that any mathematically inclined reader can fully understand. This book is truly rigorous at an introductory level, and completely bridges the gap between intuitive introductory texts and more rigorous graduate texts.

The book is divided into seven chapters and one appendix--each with four to six sections. A dozen or more exercises are given for each section. Most exercises require proofs, derivations, or written calculations. Those in chapter 3, on simulation, require writing algorithms.

Chapter 1 is titled “Combinatorics and Probability.” Chapter 2 considers specific discrete probability distributions. In chapters 3 and 4, simulation (including Markov chains and their convergence properties), sample statistics, and hypothesis tests are presented in the discrete setting. Chapters 5 and 6 introduce probability on the real line and continuous distributions. The final chapter deals with parameter estimation, including analysis of variance and linear regression.

Undoubtedly, this is an excellent and well-organized book. Every chapter contains all of the necessary definitions and formulas, including deep discussions of their meanings, proofs, and examples. This is a truly fine book on the subject, which was really needed. The book is intended for a two-semester course sequence and provides plenty of material. The preface recommends chapters and sections that can be covered in a one-semester course.

I strongly recommend this book to everyone who wants to understand probability and statistics in depth.