An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications Second edition now also available in Paperback. This updated and revised edition of the popular classic first edition relates fundamental concepts in probability and statistics to the computer sciences and engineering. The author uses Markov chains and other statistical tools to illustrate processes in reliability of computer systems and networks, fault tolerance, and performance. This edition features an entirely new section on stochastic Petri nets—as well as new sections on system availability modeling, wireless system modeling, numerical solution techniques for Markov chains, and software reliability modeling, among other subjects. Extensive revisions take new developments in solution techniques and applications into account and bring this work totally up to date. It includes more than 200 worked examples and self-study exercises for each section. Probability and Statistics with Reliability, Queuing and Computer Science Applications, Second Edition offers a comprehensive introduction to probability, stochastic processes, and statistics for students of computer science, electrical and computer engineering, and applied mathematics. Its wealth of practical examples and up-to-date information makes it an excellent resource for practitioners as well. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Table of Contents:
Preface to the Second Edition ix Preface to the First Edition xi Acronyms xiii 1 Introduction 1 1.1 Motivation 1 1.2 Probability Models 2 1.3 Sample Space 3 1.4 Events 6 1.5 Algebra of Events 7 1.6 Graphical Methods of Representing Events 11 1.7 Probability Axioms 13 1.8 Combinatorial Problems 19 1.9 Conditional Probability 23 1.10 Independence of Events 25 1.11 Bayes' Rule 38 1.12 Bernoulli Trials 45 2 Discrete Random Variables 61 2.1 Introduction 61 2.2 Random Variables and Their Event Spaces 62 2.3 The Probability Mass Function 64 2.4 Distribution Functions 66 2.5 Special Discrete Distributions 68 2.6 Analysis of Program MAX 92 2.7 The Probability Generating Function 96 2.8 Discrete Random Vectors 99 2.9 Independent Random Variables 104 3 Continuous Random Variables 115 3.1 Introduction 115 3.2 The Exponential Distribution 119 3.3 The Reliability and Failure Rate 124 3.4 Some Important Distributions 129 3.5 Functions of a Random Variable 148 3.6 Jointly Distributed Random Variables 153 3.7 Order Statistics 157 3.8 Distribution of Sums 167 3.9 Functions of Normal Random Variables 182 4 Expectation 193 4.1 Introduction 193 4.2 Moments 197 4.3 Expectation Based on Multiple Random Variables 200 4.4 Transform Methods 208 4.5 Moments and Transforms of Some Distributions 217 4.6 Computation of Mean Time to Failure 228 4.7 Inequalities and Limit Theorems 237 5 Conditional Distribution and Expectation 247 5.1 Introduction 247 5.2 Mixture Distributions 247 5.3 Conditional Expectation 262 5.4 Impefect Fault Coverage and Reliability 268 5.5 Random Sums 279 6 Stochastic Processes 289 6.1 Introduction 289 6.2 Classification of Stochastic Processes 294 6.3 The Bernoulli Process 300 6.4 The Poisson Process 304 6.5 Renewal Processes 314 6.6 Availability Analysis 319 6.7 Random Incidence 328 6.8 Renewal Model of Program Behavior 332 7 Discrete-Time Markov Chains 337 7.1 Introduction 337 7.2 Computation of n-step Transition Probabilities 341 7.3 State Classification and Limiting Probabilities 347 7.4 Distribution of Times Between State Changes 356 7.5 Markov Modulated Bernoulli Process 358 7.6 Irreducible Finite Chains with Aperiodic States 361 7.7 * The M/G/1 Queuing System 377 7.8 Discrete-Time Birth-Death Processes 385 7.9 Finite Markov Chains with Absorbing States 392 8 Continuous-Time Markov Chains 405 8.1 Introduction 405 8.2 The Birth- Death Process 412 8.3 Other Special Cases of the Birth-Death Model 446 8.4 Non-Birth-Death Processes 454 8.5 Markov Chains with Absorbing States 496 8.6 Solution Techniques 520 8.7 Automated Generation 530 9 Networks of Queues 555 9.1 Introduction 555 9.2 Open Queuing Networks 560 9.3 Closed Queuing Networks 568 9.4 General Service Distribution and Multiple Job Types 596 9.5 Non-product-form Networks 604 9.6 Computing Response Time Distribution 617 9.7 Summary 630 10 Statistical Inference 637 10.1 Introduction 637 10.2 Parameter Estimation 639 10.3 Hypothesis Testing 692 11 Regression and Analysis of Variance 727 11.1 Introduction 727 11.2 Least-squares Curve Fitting 732 11.3 The Coefficients of Determination 735 11.4 Confidence Intervals in Linear Regression 738 11.5 Trend Detection and Slope Estimation 742 11.6 Correlation Analysis 745 11. 7 Simple Nonlinear Regression 748 11.8 Higher-dimensional Least-squares Fit 749 11.9 Analysis of Variance 751 A Bibliography 765 A.1 Theory 765 A.2 Applications 770 B Properties of Distributions 777 C Statistical Tables 780 D Laplace Transforms 801 E Program Performance Analysis 808 Author Index 811 Subject Index 819