Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Edition

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 M/G/ 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