Introduction to Probability, 2nd Edition

by Dimitri P. Bertsekas and John N. Tsitsiklis

ISBN: 978-1-886529-23-6
Publication: July 2008, 544 pages, hardcover
Price: $86.00

Description:   Contents,   Preface,   Preface to the 2nd Edition,   1st Chapter,   Errata

Supplementary Material:
From the 1st Edition:  Problem Solutions (last updated 5/15/07),   Supplementary problems
For the 2nd Edition: will become available in July 2008

Link to the MIT course

Link to the MIT Open CourseWare page

Link to the translation in Chinese

Ordering, Home


An intuitive, yet precise introduction to probability theory, stochastic processes, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for "Probabilistic Systems Analysis," an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students.

The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains, a number of more advanced topics, from which an instructor can choose to match the goals of a particular course. These topics include transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics

The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis has been just intuitively explained in the text, but is developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.

This introductory book provides the foundation for many other subjects in Science and Engineering, Economics, Business, and Finance, including those dealt with in our books Neuro-Dynamic Programming (Athena Scientific, 1996), Dynamic Programming and Optimal Control (Athena Scientific, 2001), and Stochastic Optimal Control: The Discrete-Time Case (Athena Scientific, 1996).

Book Features
From the review in Analog Dialogue by Vladimir Botchev

" "trains" the intuition to acquire probabilistic feeling. This book explains every single concept it enunciates. This is its main strength, deep explanation, and not just examples that "happen" to explain."

"Tsitsiklis and Bertsekas leave nothing to… chance. The probability to misinterpret a concept or not understand it is just... zero."

"Numerous examples, figures, and end-of-chapter problems strengthen the understanding. Also of invaluable help is the book's web site, where solutions to the problems can be found-as well as much more information pertaining to probability, and also more problem sets."

Excerpts from reviews posted at

While many introductory probability texts are dominated by superficial case studies (which in my opinion convey a false sense of confidence about the subject), "Introduction to Probability" promotes deep understanding through clear mathematical writing and thought-provoking examples.

From an instructor's perspective, "Introduction to Probability" is easy to use. It is accessible to students with diverse backgrounds, and it is also well-balanced, with lots of intuitive/motivating discussion in the main body of each chapter and advanced concepts in extended end-of-the chapter problems ... I highly recommend "Introduction to Probability" to anyone preparing to teach an introductory course on stochastic systems, probability, and stochastic processes.

This book (by two well-known MIT professors of Electrical Engineering) is a wonderful treatment in terms of its style (simple informal explanations, motivating discussions, frequent notes of a historical/philosophical nature); its selection of topics (the basics, mainly, usually from the most useful perspective); its rigor and accuracy; its reasonable brevity; its rather conventional point of view (contrast it, for example, with the very interesting recent book by E. Jaynes); and its humor.

Course Adoptions

Besides MIT, this book has already been used as the primary textbook in courses offered at several universities, in the U.S., including:

U. Arizona, Boston U., CMU, Columbia U., George Mason U., Iowa State U., Middlebury College, Purdue U., RPI., Stanford U., SUNY, U. of Maryland, U. of Michigan, NorthEastern U., U. of Pennsylvania, U. of Texas at Austin, U. of Virginia, U.C. Berkeley, U.C. Davis, UCLA, Vanderbilt University, Virginia Polytechnic Institute, Worcester Polytechnic Institute

and abroad, including in Australia (Monash U.), Korea, South Africa (University of Cape Town), Taiwan, and Turkey (Bilkent, University, Isik University, Koc University).

Special Arrangements for Courses Outside of North America

Please contact us for special shipping, discount, and other arrangements for courses in universities outside of North America.

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