Probability Models

Front Cover
Springer Science & Business Media, Jul 4, 2013 - Mathematics - 287 pages

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.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Probability Spaces
1
Conditional Probability and Independence
23
Common Probability Distributions
47
Random Variables
63
Sums of Random Variables
98
Convergence and Limit Theorems
131
Stochastic Processes in Discrete Time
153
Stochastic Processes in Continuous Time
185
Appendix Common Distributions and Mathematical Facts
241
Solutions
245
Bibliography
281
Index
283
Copyright

Other editions - View all

Common terms and phrases