Probability and Statistical Inference

I have reviewed at least six textbooks during the last two years and this one is the best written of all of them. As the title says, this is really two books in one. In such books it often happens that one part is far superior to the other, if not in topical coverage, then in the love of the subject. This book does not fall into that trap; it treats both topics equally well.

The first part, probability, starts with two introductory chapters that can be safely skipped by instructors of well-prepared students. This is followed by two chapters (counting and conditional probabilities) that, very appropriately, focus on discrete probabilities. The examples, here, just as everywhere in the book, well chosen and are a pleasure to read.

After an optional chapter on Markov Chains, random variables are introduced in two chapters at a leisurely pace. Again, the balance between discrete and continuous variables is perfect. Expectation, variance, covariance, and various moments are discussed, and illustrated on some of the famous distributions, including the hypergeometric distribution. The first part of the book concludes by a chapter on Random Samples, which covers the various notions of convergence of variables and the Central Limit Theorem.

The second part, that is, the last six of sixteen chapters, is about Statistical Inference. This reviewer is a combinatorialist, and so he was prepared to be able to follow this part less well than the first part. However, thanks to the very reader-friendly style of the authors, the reviewer was pleasantly surprised. The main topics are testing hypotheses and linear models.

The only feature of the book that students may not like is its lack of full solutions to any exercises (there are numerical answers to half of them, though). This is somewhat mitigated by the large number of fully worked-out examples. On the whole, whether you are looking for a book for classroom adoption, or just want to brush up your basic probability skills by studying on your own, you will do yourself and your students a favor by considering this book.

Miklós Bóna is Associate Professor of Mathematics at the University of Florida.