Synopses & Reviews
Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics. 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 via dice and 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. No specific knowledge of the subject is assumed, only a familiarity with the notions of calculus, and the summation of series. Where the full story would call for a deeper mathematical background, the difficulties are noted and appropriate references given. The main topics arise naturally, with definitions and theorems supported by fully worked examples and some 200 set exercises, all with solutions.
Review
From the reviews: MATHEMATICAL REVIEWS "...gives a concise non-measure theoretic introduction to the basics of probability theory and stochastic processes. The overall level is that of a first university course on the subject, given that the students have had introductory courses on linear algebra and real analysis. Numerous examples make the text fairly light reading...the mathematically less trained reader will find the language (and terminology) used pleasant: no unnecessary pedantic notation is wasted. The more mathematically inclined reader will learn form both the examples and pedagogic line of approach. In summary, I find [this book] a useful text to have on my shelves and would consider using it as a textbook for science and engineering students. Mathematics students would benefit from it as a first contact with the world of randomness before delving deeper using a measure theoretic approach." ISI SHORT BOOK REVIEWS "What makes this book so interesting is the fact that, in only two hundred and fifty pages, the reader is brought from the very beginning to a fairly high level in the knowledge of probability theory. ... There is a wealth of about two hundred exercisis, with solutions, which makes the book useful for teaching." ISI Short Book Reviews, Vol. 22/3, December 2002 "'The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation'. ... this one is a nice choice, written in a broad and lively style." (P. Schmitt, Monatshefte für Mathematik, Vol. 143 (1), 2004) "A clear treatment of probability theory ... it has a great deal to recommend it. ... there is a real attempt to provide a readable account of the material without getting too bogged down in analytical detail and ... without ignoring the issues or resorting to over-simplification. ... It is good to have such specialized material in what is essentially a text for undergraduates, and I can recommend this stimulating book to anybody who is looking for a way to spice up their knowledge." (Gerry Leversha, The Mathematical Gazette, Vol. 88 (512), 2004) "What makes this book so interesting is the fact that, in only two hundred and fifty pages, the reader is brought from the very beginning to a fairly high level in the knowledge of probability theory. ... The author deals in an elegant way with important theorems such as the central limit theorem and the laws of large numbers. ... There is a wealth of about two hundred exercises, with solutions, which makes the book useful for teaching." (N.D.C. Veraverbeke, Short Book Reviews, Vol. 22 (3), 2002)
Review
From the reviews:
MATHEMATICAL REVIEWS
"...gives a concise non-measure theoretic introduction to the basics of probability theory and stochastic processes. The overall level is that of a first university course on the subject, given that the students have had introductory courses on linear algebra and real analysis. Numerous examples make the text fairly light reading...the mathematically less trained reader will find the language (and terminology) used pleasant: no unnecessary pedantic notation is wasted. The more mathematically inclined reader will learn form both the examples and pedagogic line of approach. In summary, I find [this book] a useful text to have on my shelves and would consider using it as a textbook for science and engineering students. Mathematics students would benefit from it as a first contact with the world of randomness before delving deeper using a measure theoretic approach."
ISI SHORT BOOK REVIEWS
"What makes this book so interesting is the fact that, in only two hundred and fifty pages, the reader is brought from the very beginning to a fairly high level in the knowledge of probability theory. ... There is a wealth of about two hundred exercisis, with solutions, which makes the book useful for teaching."
ISI Short Book Reviews, Vol. 22/3, December 2002
"'The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation'. ... this one is a nice choice, written in a broad and lively style." (P. Schmitt, Monatshefte für Mathematik, Vol. 143 (1), 2004)
"A clear treatment of probability theory ... it has a great deal to recommend it. ... there is a real attempt to provide a readable account of the material without getting too bogged down in analytical detail and ... without ignoring the issues or resorting to over-simplification. ... It is good to have such specialized material in what is essentially a text for undergraduates, and I can recommend this stimulating book to anybody who is looking for a way to spice up their knowledge." (Gerry Leversha, The Mathematical Gazette, Vol. 88 (512), 2004)
"What makes this book so interesting is the fact that, in only two hundred and fifty pages, the reader is brought from the very beginning to a fairly high level in the knowledge of probability theory. ... The author deals in an elegant way with important theorems such as the central limit theorem and the laws of large numbers. ... There is a wealth of about two hundred exercises, with solutions, which makes the book useful for teaching." (N.D.C. Veraverbeke, Short Book Reviews, Vol. 22 (3), 2002)
Synopsis
Includes bibliographical references (p. 227-228) and index.
Synopsis
Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics. 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 via dice and 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. No specific knowledge of the subject is assumed, only a familiarity with the notions of calculus, and the summation of series. Where the full story would call for a deeper mathematical background, the difficulties are noted and appropriate references given. The main topics arise naturally, with definitions and theorems supported by fully worked examples and some 200 set exercises, all with solutions.
Table of Contents
Preface.- 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, Mathfacts.- Bibliography.- Solutions.- Index.