Probability and Information: An Integrated Approach
Cambridge University Press
Edition: 2, 8/14/2008
EAN 9780521727884, ISBN10: 052172788X
Paperback, 290 pages, 24.7 x 17.4 x 1.4 cm
Language: English
This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to most exercises available online for instructors.
Preface to the first edition
Preface to the second edition
1. Introduction
2. Combinatorics
3. Sets and measures
4. Probability
5. Discrete random variables
6. Information and entropy
7. Communication
8. Random variables with probability density functions
9. Random vectors
10. Markov chains and their entropy
Exploring further
Appendix 1. Proof by mathematical induction
Appendix 2. Lagrange multipliers
Appendix 3. Integration of exp (-½x²)
Appendix 4. Table of probabilities associated with the standard normal distribution
Appendix 5. A rapid review of Matrix algebra
Selected solutions
Index.