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Elementary probability. 2nd, revised and updated ed. (English) Zbl 1071.60002
Cambridge University Press (ISBN 0-521-53428-3/pbk; 0-521-83344-2/hbk). xii, 524 p. (2003).
See Zbl 0784.60002 for a review of the first edition (1994).
The book consists of ten chapters and the material in the book can be grouped into three main parts, each consisting of two chapters, and four chapters with additional material. It now starts with a (new) zeroth chapter, where the basic ideas of probability and everyday experience with chance are discussed in an informal way. This chapter also presents a brief account of the history of the subject. In the next two chapters (Part 1) the fundamental concepts of probability, conditional probability, and independence are introduced. Chapter 3 is on counting, i.e., on combinatorial methods in probability. The next two chapters (Part 2) treat discrete random variables, mass functions, and expectation. Chapter 6 presents the use of probability (and other) generating functions. The next two chapters (Part 3) consider continuous random variables. The last chapter introduces the basic theory of Markov chains in discrete and continuous time. An appendix contains solutions and hints for selected exercises. As in the first edition, a large number of examples and exercises accompany the material in each chapter. Also, each chapter now has a section entitled ‘Review and checklist’. Further, some additional topics have been included: elementary introductions to martingales, Brownian motion, diffusion, and the Wiener process, as well as optional stopping and its applications in the context of these important stochastic models. As the first edition, the book is very well written, in a clear, detailed and readable style. It is accessible for undergraduate students and would make a good textbook for first courses on probability or for self-study.

MSC:
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60A99 Foundations of probability theory
60C05 Combinatorial probability
60G42 Martingales with discrete parameter
60G44 Martingales with continuous parameter
60G15 Gaussian processes
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J27 Continuous-time Markov processes on discrete state spaces
60J60 Diffusion processes
60J65 Brownian motion
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