Probability Models

An introduction to probability for undergraduate students, this book draws on everyday experience (games with dice; weather patterns, betting on sports events), and includes a wide range of problems and exercises, from the routine to the more challenging, for self-study.

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"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.