Elementary Probability

Rating:
Summary: Excellent probability book
Review: The book is organized so as to discuss probability, discrete random variables, and then continuous random variables carefully.
The last chapter is on Markov chains, however the reader will recognize that random processes have been introduced in examples before. This book contains wonderful examples. The examples are marked by level of difficulty. Some examples appear under several topics, this higlights different aspects and gives a deeper understanding. This book is a pleasure to read. You won't regret reading this book carefully, but it cannot be used as a "reference book" for theorems. Instead it is more a reference book for examples, where different examples highlight several aspects of a topic, some of which you may not have thought of on your own.
The author is very precise in the formulation of the problems and mathematics (unlike other authors).

I particular like his discussion of the Monty Hall problem that has caused so much disagreements due to imprecise formulation in the press.

Beware the word "elementary" in the title refers to probability topics. It has never been true that "elementary" means "easy!"

Rating:
Summary: one of the best, but not for everyone
Review: The book is well organized...however it is written for mathematicians (sorry, engineers and other scientists!). In other words, the book is neither elementary (as the title suggests) nor application-oriented. All the necessary elements of the theory are here, if you know how to find them. Good and challenging exercises.

Rating:
Summary: Interesting but hard to read
Review: This book has interesting, lively analysis and examples. However, it is hard to read for a number of reasons. Some of them (complex sentences, loose organization) have been pointed out by other reviewers). There is another flaw, which is particularly annoying if you want to use the book as a reference: the author tends to jump into a new section without a roadmap for the reader or a connection with earlier sections. As a result, it is hard to start reading a new section without first reading the preceding section.