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 Second Edition ixPreface to the First Edition xiAcronyms xiii1 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 231.10 Independence of Events 251.11 Bayes' Rule 381.12 Bernoulli Trials 452 Discrete Random Variables 612.1 Introduction 612.2 Random Variables and Their Event Spaces 622.3 The Probability Mass Function 642.4 Distribution Functions 662.5 Special Discrete Distributions 682.6 Analysis of Program MAX 922.7 The Probability Generating Function 962.8 Discrete Random Vectors 992.9 Independent Random Variables 1043 Continuous Random Variables 1153.1 Introduction 1153.2 The Exponential Distribution 1193.3 The Reliability and Failure Rate 1243.4 Some Important Distributions 1293.5 Functions of a Random Variable 1483.6 Jointly Distributed Random Variables 1533.7 Order Statistics 1573.8 Distribution of Sums 1673.9 Functions of Normal Random Variables 1824 Expectation 1934.1 Introduction 1934.2 Moments 1974.3 Expectation Based on Multiple Random Variables 2004.4 Transform Methods 2084.5 Moments and Transforms of Some Distributions 2174.6 Computation of Mean Time to Failure 2284.7 Inequalities and Limit Theorems 2375 Conditional Distribution and Expectation 2475.1 Introduction 2475.2 Mixture Distributions 2475.3 Conditional Expectation 2625.4 Impefect Fault Coverage and Reliability 2685.5 Random Sums 2796 Stochastic Processes 2896.1 Introduction 2896.2 Classification of Stochastic Processes 2946.3 The Bernoulli Process 3006.4 The Poisson Process 3046.5 Renewal Processes 3146.6 Availability Analysis 3196.7 Random Incidence 3286.8 Renewal Model of Program Behavior 3327 Discrete-Time Markov Chains 3377.1 Introduction 3377.2 Computation of n-step Transition Probabilities 3417.3 State Classification and Limiting Probabilities 3477.4 Distribution of Times Between State Changes 3567.5 Markov Modulated Bernoulli Process 3587.6 Irreducible Finite Chains with Aperiodic States 3617.7 * The M/G/1 Queuing System 3777.8 Discrete-Time Birth-Death Processes 3857.9 Finite Markov Chains with Absorbing States 3928 Continuous-Time Markov Chains 4058.1 Introduction 4058.2 The Birth- Death Process 4128.3 Other Special Cases of the Birth-Death Model 4468.4 Non-Birth-Death Processes 4548.5 Markov Chains with Absorbing States 4968.6 Solution Techniques 5208.7 Automated Generation 5309 Networks of Queues 5559.1 Introduction 5559.2 Open Queuing Networks 5609.3 Closed Queuing Networks 5689.4 General Service Distribution and Multiple Job Types 5969.5 Non-product-form Networks 6049.6 Computing Response Time Distribution 6179.7 Summary 63010 Statistical Inference 63710.1 Introduction 63710.2 Parameter Estimation 63910.3 Hypothesis Testing 69211 Regression and Analysis of Variance 72711.1 Introduction 72711.2 Least-squares Curve Fitting 73211.3 The Coefficients of Determination 73511.4 Confidence Intervals in Linear Regression 73811.5 Trend Detection and Slope Estimation 74211.6 Correlation Analysis 74511. 7 Simple Nonlinear Regression 74811.8 Higher-dimensional Least-squares Fit 74911.9 Analysis of Variance 751A Bibliography 765A.1 Theory 765A.2 Applications 770B Properties of Distributions 777C Statistical Tables 780D Laplace Transforms 801 E Program Performance Analysis 808 Author Index 811Subject Index 819