Probability and Statistics with Reliability, Queuing, and Computer Science Applications

Kishor S. Trivedi, PhD, is the Hudson Professor of Electrical and Computer Engineering at Duke University, Durham, North Carolina. His research interests are in reliability and performance assessment of computer and communication systems. Dr. Trivedi has published extensively in these fields, with more than 600 articles and three books to his name. Dr. Trivedi is a Fellow of the IEEE and a Golden Core Member of the IEEE Computer Society.

"The book 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." (Zentralblatt MATH, 2016)"I highly recommend this book for academics for use as a textbook and for researchers and professionals in the field as a useful reference." (Interfaces, September/ October 2004)"This introduction...uses Markov chains and other statistical tools to illustrate process in reliability of computer systems, fault tolerance, and performance." (SciTech Book News, Vol. 26, No. 2, June 2002)"...an excellent self-contained book.... I recommend the book to beginners and veterans in the field..." (Computer Journal, Vol.45, No.6, 2002)"This book is a tour de force of clear, virtually error-free exposition of probability as it is applied in a host of up-to-date contexts.... It will richly reward the...reader.... Read this book cover to cover. It’s worth the effort." (Technometrics, Vol. 45, No. 1, February 2003)

• Preface to the Paperback Edition ixPreface to the Second Edition xiPreface to the First Edition xiiiAcronyms xvAbout the Companion Website xix1 Introduction 11.1 Motivation 11.2 Probability Models 21.3 Sample Space 31.4 Events 61.5 Algebra of Events 71.6 Graphical Methods of Representing Events 111.7 Probability Axioms 131.8 Combinatorial Problems 191.9 Conditional Probability 241.10 Independence of Events 261.11 Bayes’ Rule 381.12 Bernoulli Trials 472 Discrete Random Variables 652.1 Introduction 652.2 Random Variables and Their Event Spaces 662.3 The Probability Mass Function 682.4 Distribution Functions 702.5 Special Discrete Distributions 722.6 Analysis of Program MAX 972.7 The Probability Generating Function 1012.8 Discrete Random Vectors 1042.9 Independent Random Variables 1103 Continuous Random Variables 1213.1 Introduction 1213.2 The Exponential Distribution 1253.3 The Reliability and Failure Rate 1303.4 Some Important Distributions 1353.5 Functions of a Random Variable 1543.6 Jointly Distributed Random Variables 1593.7 Order Statistics 1633.8 Distribution of Sums 1743.9 Functions of Normal Random Variables 1904 Expectation 2014.1 Introduction 2014.2 Moments 2054.3 Expectation Based on Multiple Random Variables 2094.4 Transform Methods 2164.5 Moments and Transforms of Some Distributions 2264.6 Computation of Mean Time to Failure 2384.7 Inequalities and Limit Theorems 2475 Conditional Distribution and Expectation 2575.1 Introduction 2575.2 Mixture Distributions 2665.3 Conditional Expectation 2735.4 Imperfect Fault Coverage and Reliability 2805.5 Random Sums 2906 Stochastic Processes 3016.1 Introduction 3016.2 Classification of Stochastic Processes 3076.3 The Bernoulli Process 3136.4 The Poisson Process 3176.5 Renewal Processes 3276.6 Availability Analysis 3326.7 Random Incidence 3426.8 Renewal Model of Program Behavior 3467 Discrete-Time Markov Chains 3517.1 Introduction 3517.2 Computation of n-step Transition Probabilities 3567.3 State Classification and Limiting Probabilities 3627.4 Distribution of Times Between State Changes 3717.5 Markov Modulated Bernoulli Process 3737.6 Irreducible Finite Chains with Aperiodic States 3767.7 The M/G/ 1 Queuing System 3917.8 Discrete-Time Birth–Death Processes 4007.9 Finite Markov Chains with Absorbing States 4078 Continuous-Time Markov Chains 4218.1 Introduction 4218.2 The Birth–Death Process 4288.3 Other Special Cases of the Birth–Death Model 4658.4 Non-Birth–Death Processes 4748.5 Markov Chains with Absorbing States 5198.6 Solution Techniques 5418.7 Automated Generation 5529 Networks of Queues 5779.1 Introduction 5779.2 Open Queuing Networks 5829.3 Closed Queuing Networks 5909.4 General Service Distribution and Multiple Job Types 6209.5 Non-product-form Networks 6289.6 Computing Response Time Distribution 6419.7 Summary 65410 Statistical Inference 66110.1 Introduction 66110.2 Parameter Estimation 66310.3 Hypothesis Testing 71811 Regression and Analysis of Variance 75311.1 Introduction 75311.2 Least-squares Curve Fitting 75811.3 The Coefficients of Determination 76211.4 Confidence Intervals in Linear Regression 76511.5 Trend Detection and Slope Estimation 76811.6 Correlation Analysis 77111.7 Simple Nonlinear Regression 77411.8 Higher-dimensional Least-squares Fit 77511.9 Analysis of Variance 778A Bibliography 791A.1 Theory 791A.2 Applications 796B Properties of Distributions 804C Statistical Tables 807D Laplace Transforms 828E Program Performance Analysis 835Author Index 837Subject Index 845