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.
