# Probability and Statistics for Computer Science

ISBN: 978-0-470-38342-1
760 pages
May 2008
Comprehensive and thorough development of both probability and statistics for serious computer scientists; goal-oriented: "to present the mathematical analysis underlying probability results"
Special emphases on simulation and discrete decision theory
Mathematically-rich, but self-contained text, at a gentle pace
Review of calculus and linear algebra in an appendix
Mathematical interludes (in each chapter) which examine mathematical techniques in the context of probabilistic or statistical importance
Numerous section exercises, summaries, historical notes, and Further Readings for reinforcement of content
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Preface.

1. Combinatorics and Probability.

1.1 Combinatorics.

1.2 Summations.

1.3 Probability spaces and random variables.

1.4 Conditional probability.

1.5 Joint distributions.

1.6 Summary.

2. Discrete Distributions.

2.1 The Bernoulli and binomial distributions.

2.2 Power series.

2.3 Geometric and negative binomial forms.

2.4 The Poisson distribution.

2.5 The hypergeometric distribution.

2.6 Summary.

3. Simulation.

3.1 Random number generation.

3.2 Inverse transforms and rejection filters.

3.3 Client-server systems.

3.4 Markov chains.

3.5 Summary.

4. Discrete Decision Theory.

4.1 Decision methods without samples.

4.2 Statistics and their properties.

4.3 Sufficient statistics.

4.4 Hypothesis testing.

4.5 Summary.

5. Real Line-Probability.

5.1 One-dimensional real distributions.

5.2 Joint random variables.

5.3 Differentiable distributions.

5.4 Summary.

6. Continuous Distributions.

6.1 The normal distributions.

6.2 Limit theorems.

6.3 Gamma and beta distributions.

6.4 The X2 and related distributions.

6.5 Computer simulations.

6.6 Summary.

7. Parameter Estimation.

7.1 Bias, consistency, and efficiency.

7.2 Normal inference.

7.3 Sums of squares.

7.4 Analysis of variance.

7.5 Linear regression.

7.6 Summary.

A. Analytical Tools.

B. Statistical Tables.

Bibliography.

Index.

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James L. Johnson holds a PhD in mathematics from the University of Minnesota and has twenty-five years' experience in academic and industrial computer science. He is currently Professor of Computer Science at Western Washington University. He is also the author of Database: Models, Languages, Design.
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"Undoubtedly, this is an excellent and well-organized book." (Computing Reviews, August 27, 2008)
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