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.

Very suitable for self-study Provides many worked examples and exercises Suitable for beginners; no prior knowledge of probability is needed Includes supplementary material: sn.pub/extras

Autorentext

John Haigh set up the class "Mathematics In Everyday Life" at Sussex University in 2005, in response to a desire to show first year students some of the areas where their mathematical skills and knowledge could provide useful insight, and to give them practice in applying the mathematics they were learning on other modules. This book has benefited from the feedback of several cohorts of students. John has also written the well-received popular science book "Taking Chances" and, with Rob Eastaway, "The Hidden Mathematics of Sport".

Zusammenfassung
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.

Inhalt
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.