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: $91.00

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An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, 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, 2007), and Stochastic Optimal Control: The Discrete-Time Case (Athena Scientific, 1996).

• The 2nd Edition includes two new chapters with a thorough coverage of the central ideas of Bayesian and classical statistics.

• Develops the basic concepts of probability, random variables, stochastic processes, laws of large numbers, and the central limit theorem

• Illustrates the theory with many examples

• Provides many theoretical problems that extend the book's coverage and enhance its mathematical foundation (solutions are included in the text)

• Provides many problems that enhance the understanding of the basic material, together with web-posted solutions

• Is supplemented by additional web-based unsolved problems.

• Is coordinated with the material (syllabus, lecture slides, selection of homework, recitation, and tutorial problems) that is used in the MIT course, and can help an instructor design his/her own course.

• Has been developed through extensive classroom use and experience at the Massachusetts Institute of Technology

"...it "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 Amazon.com of the 1st edition and the 2nd edition

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.

This is a must buy for people who would like to learn elementary probability. The only background you need is basic series and calculus. This is the best probability book I have seen.

This is an outstanding book that helps to make the subject of probability come alive ... Indeed, even those studying probability from a more theoretical standpoint may find this book useful as a supplementary resource ... It is a terrific resource for instructors looking for ways to illustrate probabilistic concepts to their students (this is the capacity in which I have used the book). With the addition of the chapters on statistical inference in the second edition, it is likely to be a valuable reference for practitioners as well, particularly those seeking to refresh the connections between statistical methods and basic probability.

The chapter on estimation, added for the second edition, is some of the most interesting material in the book, and covers both frequentist and bayesian estimation.

Having skimmed various other textbooks while teaching a semester-long course with this one six times, I have come to believe that there is a large audience for which this is the best available textbook.

Because of a disciplined avoidance of unnecessary mathematical technicalities and flourishes, the book has a fast pace without being difficult to read. The end result is a solid grounding in the foundations of probability along with introductions to random processes and statistical inference in a remarkably concise volume.

Written by two professors of the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology, and members of the prestigious US National Academy of Engineering, the book has been widely adopted for classroom use in introductory probability courses in the U.S., including:

U. Arizona, Boston U., Brigham Young U., State U. of New York at Buffalo, Carnegie Mellon U., Claremont McKenna College, Columbia U., Cornell U., George Mason U., Iowa State U., George Washington U., Middlebury College, Purdue U., RPI, Stanford U., SUNY, U. of Maryland, U. of Michigan, NorthEastern U., U. of Pennsylvania, Rice U., U. of Texas at Austin, U. of Toronto, Towson U., 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).

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