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Probability, statistics, and stochastic processes. (English) Zbl 1080.60001

Hoboken, NJ: John Wiley & Sons (ISBN 0-471-67969-0/hbk; 978-0-471-74306-4/ebook). xi, 486 p. (2005).
This textbook provides a unique, balanced approach to probability, statistics and stochastic processes. This text combines a rigorous, calculus based development of the theory.
The book contains seven chapters. The first chapter “Basic probability theory” intoduces the axioms of probability, conditional probability and independence, the law of total probability and Bayes’ formula. The second chapter “Random variables” contains discrete and continuous random variables, the uniform distribution, expected value and variance, special discrete distributions, the exponential and normal and also other distributions. Chapter three is entitled “Joint distributions” and begins with the joint distributions, conditional distributions and independence, conditional expectation, multidimensional random vectors, generating functions and the Poisson process. The next two chapters introduce limit theorems and simulation. In chapter six on statistical inference with confidence intervals, estimation methods, hypothesis testing, linear regression, Bayesian methods and others are included. Stochastic processes are dicussed in Chapter seven, which contains discrete-time Markov chains, random walks and branching processes, continuous time Markov chains with birth-depth processes, queueing theory, further properties of queueing systems.
More than 400 examples are interspersed throughout the text to help to illustrate concepts and theory and to assist the readers in developing an intuitive sense of the subject. Readers will find many of the examples to be both entertaining and thought provoking. This is also true for the carefully selected problems that appear at the end of each chapter. The last part of the book contains the tables of different distributions, answers to selected problems, references and an index.
This book is an excellent text for upperlevel undergraduate courses. Because it is addressed to students in science and engineering, I consider necessarily to introduce in the bibliography a great number of titles, for example: A. T. Bharucha-Reid [“Elements of the theory of Markov processes and their applications” (1960; Zbl 0095.32803)]; P. P. Bocharov, C. D’Aprice, A. V. Pechinkin and S. Salerno [“Queueing theory” (2004; Zbl 1061.60093)]; H. Crawer [“Mathematical methods of statistics” (Princeton, 1954)]; W. Feller [“An introduction to probability theory and its applications”. Vol. 1 (1957; Zbl 0077.12201), Vol. 2 (1966; Zbl 0138.10207)]; M. Iosifescu and P. Tătu [“Stochastic processes and applications in biology and medicine” (Berlin, 1973)]; A. Rényi [“Calcul des probabilités” (1966; Zbl 0141.14702)].

MSC:

60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
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