You are previewing Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Edition.
O'Reilly logo
Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Edition

Book Description

An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications

This updated and revised edition of the popular classic 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

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface to the Paperback Edition
  5. Preface to the Second Edition
  6. Preface to the First Edition
  7. Acronyms
  8. About the Companion Website
  9. Chapter 1: Introduction
    1. 1.1 Motivation
    2. 1.2 Probability Models
    3. 1.3 Sample Space
    4. 1.4 Events
    5. 1.5 Algebra of Events
    6. 1.6 Graphical Methods of Representing Events
    7. 1.7 Probability Axioms
    8. 1.8 Combinatorial Problems
    9. 1.9 Conditional Probability
    10. 1.10 Independence of Events
    11. 1.11 Bayes' Rule
    12. 1.12 Bernoulli Trials
    13. References
  10. Chapter 2: Discrete Random Variables
    1. 2.1 Introduction
    2. 2.2 Random Variables and Their Event Spaces
    3. 2.3 The Probability Mass Function
    4. 2.4 Distribution Functions
    5. 2.5 Special Discrete Distributions
    6. 2.6 Analysis of Program MAX
    7. 2.7 The Probability Generating Function
    8. 2.8 Discrete Random Vectors
    9. 2.9 Independent Random Variables
    10. References
  11. Chapter 3: Continuous Random Variables
    1. 3.1 Introduction
    2. 3.2 The Exponential Distribution
    3. 3.3 The Reliability and Failure Rate
    4. 3.4 Some Important Distributions
    5. 3.5 Functions of a Random Variable
    6. 3.6 Jointly Distributed Random Variables
    7. 3.7 Order Statistics
    8. 3.8 Distribution of Sums
    9. 3.9 Functions of Normal Random Variables
    10. References
  12. Chapter 4: Expectation
    1. 4.1 Introduction
    2. 4.2 Moments
    3. 4.3 Expectation Based on Multiple Random Variables
    4. 4.4 Transform Methods
    5. 4.5 Moments and Transforms of Some Distributions
    6. 4.6 Computation of Mean Time to Failure
    7. 4.7 Inequalities and Limit Theorems
    8. References
  13. Chapter 5: Conditional Distribution and Expectation
    1. 5.1 Introduction
    2. 5.2 Mixture Distributions
    3. 5.3 Conditional Expectation
    4. 5.4 Imperfect Fault Coverage and Reliability
    5. 5.5 Random Sums
    6. References
  14. Chapter 6: Stochastic Processes
    1. 6.1 Introduction
    2. 6.2 Classification of Stochastic Processes
    3. 6.3 The Bernoulli Process
    4. 6.4 The Poisson Process
    5. 6.5 Renewal Processes
    6. 6.6 Availability Analysis
    7. 6.7 Random Incidence
    8. 6.8 Renewal Model of Program Behavior
    9. References
  15. Chapter 7: Discrete-Time Markov Chains
    1. 7.1 Introduction
    2. 7.2 Computation of n-step Transition Probabilities
    3. 7.3 State Classification and Limiting Probabilities
    4. 7.4 Distribution of Times Between State Changes
    5. 7.5 Markov Modulated Bernoulli Process
    6. 7.6 Irreducible Finite Chains with Aperiodic States
    7. 7.7 * The <i xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ibooks="http://vocabulary.itunes.apple.com/rdf/ibooks/vocabulary-extensions-1.0">M</i>//<i xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ibooks="http://vocabulary.itunes.apple.com/rdf/ibooks/vocabulary-extensions-1.0">G</i>/ 1 Queuing System/ 1 Queuing System
    8. 7.8 Discrete-Time Birth–Death Processes
    9. 7.9 Finite Markov Chains with Absorbing States
    10. References
  16. Chapter 8: Continuous-Time Markov Chains
    1. 8.1 Introduction
    2. 8.2 The Birth–Death Process
    3. 8.3 Other Special Cases of the Birth–Death Model
    4. 8.4 Non-Birth–Death Processes
    5. 8.5 Markov Chains with Absorbing States
    6. 8.6 Solution Techniques
    7. 8.7 Automated Generation
    8. References
  17. Chapter 9: Networks of Queues
    1. 9.1 Introduction
    2. 9.2 Open Queuing Networks
    3. 9.3 Closed Queuing Networks
    4. 9.4 General Service Distribution and Multiple Job Types
    5. 9.5 Non-product-form Networks
    6. 9.6 Computing Response Time Distribution
    7. 9.7 Summary
    8. References
  18. Chapter 10: Statistical Inference
    1. 10.1 Introduction
    2. 10.2 Parameter Estimation
    3. 10.3 Hypothesis Testing
    4. References
  19. Chapter 11: Regression and Analysis of Variance
    1. 11.1 Introduction
    2. 11.2 Least-squares Curve Fitting
    3. 11.3 The Coefficients of Determination
    4. 11.4 Confidence Intervals in Linear Regression
    5. 11.5 Trend Detection and Slope Estimation
    6. 11.6 Correlation Analysis
    7. 11.7 Simple Nonlinear Regression
    8. 11.8 Higher-dimensional Least-squares Fit
    9. 11.9 Analysis of Variance
    10. References
  20. Appendix A: Bibliography
    1. A.1 Theory
    2. A.2 Applications
  21. Appendix B: Properties of Distributions
  22. Appendix C: Statistical Tables
  23. Appendix D: Laplace Transforms
    1. References
  24. Appendix E: Program Performance Analysis
  25. Author Index
  26. Subject Index
  27. End User License Agreement