Introduction to Probability Theory

The authors introduce the most elementary ideas of probability theory in quite a few pages. They include the right amount of examples to clarify the concepts without making the exposition too tedious. To make the story short: if you want to learn elementary probability as fast as possible without loosing the essentials, get this book.

I agree with everything other reviewers have said about this book and more.

I first noticed this book during the time that I spent at UC Berkeley as an undergraduate applied mathematics major. It was being used for Stat 101, and though I was not taking that course, I bought it because it looked even from casual inspection to be very well laid out, covering important and interesting issues in basic probability. The strongest feature of this book from my point of view is its conciseness. Much is presented in as short a time as possible, and because of that the book is much more readable than many others of its level. In addition to conciseness, the authors (in my edition Hoel, Port, and Stone) have made a commendable effort to present the reader with clear and concrete definitions, compact theorems (many proven), and abundant useful examples. In the back of the book nearly all of the solutions of the chapter exercises are given, unlike many books where answers to only the odd problems are given. I believe that this book is ideal for self-study, and that much use of it could also be made as a textbook for an undergraduate course in probability. The exercises are not very difficult, but they are by no means trivial, and much can be learned from them. At the end of a close study of this book the reader would be ready to enter into a program of undergraduate level mathematical statistics, or into a further study of probability with the confidence inspired by a firm understanding of the most fundamental and key concepts in probability theory.

This was the book used in the standard upper-division probability course at UC Berkeley when I took it 18 years ago. In my opinion it is still the best. I have since taught the subject myself and was forced to use other books, with many more pages and fancy pictures than Hoel's book. Yet those books do not do anywhere near as good a job of teaching probabilistic *thinking* as well as Hoel. This is what causes the most problems for students of probability, and Hoel does it the right way in Chapters 1 and 2, which are key. The basic explanations are clear and concise, with many instructive examples.My professor back then told us that if we want to learn probability, then do every exercise in this book. She was absolutely right. The exercises are excellent. Do them, and you will learn a lot.This used to be *the* book on elementary calculus-based probability theory at most universities. I don't understand why it seems to have fallen out of favor. Perhaps because of its size (it is fairly compact, as it should be) and age, though I fear that it may be because it is a bit more demanding (but worth it) than many of the newer books.

This classical text is complete and detailed. I'm an undergraduate and used the book after acquiring the basics of multiple integration as an introduction to the calculus of probability. Plenty of exercises (answers provided) which not only help you understanding the theory but are also complementary to the text. (This is a "non-measure" text on probability theory.) Well written!!!! (see also Hoel at al., 'Int. to Stochastic Processes', and Taylor, 'An Int. to Measure and Probability',(Springer-Verlag)).