Probability and Statistics for Computer Scientists: Trim size is 6 1/2 x 9 1/2: Baron, Michael: 9781584886419: Book: Technology: eCampus.com

1 Introduction and Overview

1.1 Making decisions under uncertainty

1.2 Overview of this book

2 Probability

2.1 Sample space, events, and probability

2.2 Rules of Probability

2.3 Equally likely outcomes. Combinatorics

2.4 Conditional probability. Independence

3 Discrete Random Variables and their Distributions

3.1 Distribution of a random variable

3.2 Distribution of a random vector

3.3 Expectation and variance

3.4 Families of discrete distributions

4 Continuous Distributions

4.1 Probability density

4.2 Families of continuous distributions

4.3 Central Limit Theorem

100

5 Computer Simulations and Monte Carlo Methods

111

5.1 Introduction

111

5.2 Simulation of random variables

114

5.3 Solving problems by Monte Carlo methods

126

6 Stochastic Processes

143

6.1 Definitions and Classifications

143

6.2 Markov processes and Markov chains

145

6.3 Counting processes

162

6.4 Simulation of stochastic processes

172

7 Queuing Systems

183

7.1 Main components of a queuing system

183

7.2 The Little's Law

186

7.3 Bernoulli single-server queuing process

189

7.4 M/M/1 system

195

7.5 Multiserver queuing systems

202

7.6 Simulation of queuing systems

212

8 Introduction to Statistics

221

8.1 Population and sample, parameters and statistics

222

8.2 Simple descriptive statistics

224

8.3 Graphical statistics

238

9 Statistical Inference

253

9.1 Parameter estimation

253

9.2 Confidence intervals

262

9.3 Unknown standard deviation

270

9.4 Hypothesis testing

282

9.5 Bayesian estimation and hypothesis testing

305

10 Regression

327

10.1 Least squares estimation

327

10.2 Analysis of variance, prediction, and further inference

335

10.3 Multivariate regression

348

10.4 Model building

358

11 Appendix

371

11.1 Inventory of distributions

371

11.2 Distribution tables

377

11.3 Calculus review

391

11.4 Matrices and linear systems

398

11.5 Answers to selected exercises

404

Index

409


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