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Book Review
Introduction to Probability by Dimitri P. Bertsekas and John N. Tsitsiklis, Athena Scientific Publishers 2002, ISBN 1-886529-40-X
Reviewed by Vladimir Botchev [vladimir.botchev@analog.com]
This book should have had an addendum to its main title; “a unique introduction for engineers.” I wish this text had been available to me years ago, when trying to teach a similar subject. The main reference at that time was Introduction to Probability, by J. Laurie Snell (Birkhauser, 1988), beautifully written but a hard nut to crack for students. The Tsitsiklis and Bertsekas book is perhaps the best available introduction to date. Probabilistic calculations permeate signal- and image-processing engineering, communications engineering, and control engineering—to cite a few of the top “users”. A solid foundation and friendly refresher is extremely helpful on this somewhat evasive (for newcomers especially) mathematical discipline. Of course, there exists a landmark text, Probability, Random Variables and Stochastic Processes by Papoulis, however this latter, much more formal than intuitive, is hardly for beginners.
In line with the famous quotation from Laplace, “Probability theory is nothing but common sense reduced to calculation,” intuition should be “trained” to probability concepts as a prerequisite for one to become conversant with formal techniques. The Tsitsiklis and Bertsekas book does exactly that—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. This approach is also a feature of Snell’s book, but often it would just begin an explanation but leave the continuation of it to the reader. Tsitsiklis and Bertsekas leave nothing to… chance. The probability to misinterpret a concept or not understand it is just… zero.
An example of authors' intuitive approach can be seen in the hard-to-explain-to-newcomers concept of events being both uncorrelated and non-independent. The example on page 237, although almost classical, is rephrased in such a way that it is strikingly obvious that the joint “wiggles” (i.e., variance) of two random variables could very well be zero, but every concrete value of one of them forces the other to take its value from a well-identified subset and not from anywhere else—which is of course what one calls dependency.
Seven chapters, on initial probability concepts—based mainly on counting principles and combinatorics, two on basics of random variables, one on more-advanced random-variables topics, and one on each of the following: Bernoulli/Poisson processes, Markov chains and limit theorems form the core of the book. 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.
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