Probability and Statistics for Computer Science

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.