Probability and information : an integrated approach
著者
書誌事項
Probability and information : an integrated approach
Cambridge University Press, 1996
- : hbk
- : pbk
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注記
Includes bibliographical referebces and index
内容説明・目次
内容説明
This elementary introduction to probability theory and information theory is suitable as a textbook for beginning students in mathematics, statistics or computer science who have some knowledge of basic calculus. It provides a clear and systematic foundation to the subject; the concept of probability is given particular attention via a highly 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 dealt with include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information. Many examples and exercises are included that illustrate how the theory can be applied, for example to information technology. Detailed solutions to most exercises are available electronically from the Cambridge WWW server.
目次
- Preface
- 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
- Exploring further
- Appendix 1: Proof by induction
- Appendix 2: Lagrange multipliers
- Appendix 3: Integration of exp(-x2/2)
- Appendix 4: Table of probabilities associated with the standard normal distribution
- Solutions to selected exercises.
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