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Macmillan Higher Education Palgrave Higher Education

Probability Models

Edition 2nd Edition
ISBN 9781447153429
Publication Date July 2013
Formats Paperback Ebook 
Publisher Springer

The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise.

Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. This textbook contains many worked examples and several chapters have been updated and expanded for the second edition. 

Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logical development of an argument. Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics.

Probability Spaces
Conditional Probability and Independence
Common Probability Distributions
Random Variables
Sums of Random Variables
Convergence and Limit Theorems
Stochastic Processes in Discrete Time
Stochastic Processes in Continuous Time
Appendix: Common Distributions and Mathematical Facts.


From the reviews of the second edition:“It should be on the desk of any university teacher and anybody studying probability and stochastic processes. … there are exercises given in the end of each chapter. Solutions or good hints are summarised and located at the end of the book. All these make the book more than useful to a wide spectrum of readers. For anybody needing a good introduction to modern probability and stochastic processes, this is the book to start with.” (Jordan M. Stoyanov, zbMATH, Vol. 1286, 2014)“This is an introductory book on probabilistic modeling that I can recommend to any student or teacher. It is not only for probability courses, but also for general mathematics, since the proofs, definitions, and examples are so beautifully intermingled and interspersed.” (Arturo Ortiz-Tapia, Computing Reviews, November, 2013)
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