Introduction to Probability Models, Sixth Edition

✍ Scribed by Sheldon M. Ross

• Publisher: Academic Press
• Year: 1997
• Tongue: English
• Leaves: 663
• Edition: 6
• Category: Library

✦ Synopsis

The Sixth Edition of this very successful textbook, Introduction to Probability Models<$>, introduces elementary probability theory and stochastic processes. This book is particularly well-suited for those who want to see how probability theory can be applied to the study of phenomena in fields such as engineering, management science, the physical and social sciences, and operations research. The Sixth Edition includes additional exercises in every chapter and a new appendix with the answers to approximately 100 of the included exercises from throughout the text. Markov Chain Monte Carlo methods are presented in an entirely new section, along with new coverage of the Markov Chain cover times. New material will also be featured on K-records values and Ignatov's theorem. This book is a worthwhile revision of Ross's classic text. Presents new material in every chapter Contains examples relating to: Random walks on circles The matching rounds problem The best prize problem K-records values Ignatovs theorem Includes approximately 570 exercises Provides a built-in student solution manual in the appendix for 100 of the exercises from throughout the book An instructors manual, containing solutions to all exercises, is available free of charge for instructors who adopt the book for their classes

✦ Table of Contents

Contents......Page 5
Preface to the Sixth Edition......Page 11
Preface to the Fifth Edition......Page 13
1.2. Sample Space and Events......Page 17
1.3. Probabilities Defined on Events......Page 20
1.4. Conditional Probabilities......Page 23
1.5. Independent Events......Page 26
1.6. Bayes' Formula......Page 28
Exercises 1......Page 31
References......Page 36
2.1. Random Variables......Page 37
2.2. Discrete Random Variables......Page 41
2.2.2. The Binomial Random Variable......Page 42
2.2.3. The Geometric Random Variable......Page 45
2.2.4. The Poisson Random Variable......Page 46
2.3. Continuous Random Variables......Page 47
2.3.1. The Uniform Random Variable......Page 48
2.3.4. Normal Random Variables......Page 50
2.4.1. The Discrete Case......Page 52
2.4.2. The Continuous Case......Page 55
2.4.3. Expectation of a Function of a Random Variable......Page 56
2.5.1. Joint Distribution Functions......Page 60
2.5.2. Independent Random Variables......Page 64
2.5.3. Covariance and Variance of Sums of Random Variables......Page 65
2.5.4. Joint Probability Distribution of Functions of Random Variables......Page 74
2.6. Moment Generating Functions......Page 76
2.6.1. The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population......Page 84
2.7. Limit Theorems......Page 87
2.8. Stochastic Processes......Page 93
Exercises 2......Page 95
References......Page 106
3.2. The Discrete Case......Page 107
3.3. The Continuous Case......Page 112
3.4. Computing Expectations by Conditioning......Page 115
3.5. Computing Probabilities by Conditioning......Page 127
3.6.1. A List Model......Page 140
3.6.2. A Random Graph......Page 142
3.6.3. Uniform Priors, Polya's Urn Model, and Bose-Einstein Statistics......Page 149
3.6.4. The k-Record Values of Discrete Random Variables......Page 153
Exercises 3......Page 157
4.1. Introduction......Page 175
4.2. Chapman-Kolmogorov Equations......Page 178
4.3. Classification of States......Page 181
4.4. Limiting Probabilities......Page 190
4.5.1. The Gambler's Ruin Problem......Page 201
4.5.2. A Model for Algorithmic Efficiency......Page 204
4.5.3. Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem......Page 207
4.6. Mean Time Spent in Transient States......Page 213
4.7. Branching Processes......Page 215
4.8. Time Reversible Markov Chains......Page 219
4.9. Markov Chain Monte Carlo Methods......Page 229
4.10. Markov Decision Processes......Page 235
Exercises 4......Page 239
References......Page 252
5.1. Introduction......Page 253
5.2.1. Definition......Page 254
5.2.2. Properties of the Exponential Distribution......Page 255
5.2.3. Further Properties of the Exponential Distribution......Page 260
5.2.4. Convolutions of Exponential Random Variables......Page 263
5.3.1. Counting Processes......Page 267
5.3.2. Definition of the Poisson Process......Page 268
5.3.3. Interarrival and Waiting Time Distributions......Page 273
5.3.4. Further Properties of Poisson Processes......Page 275
5.3.5. Conditional Distribution of the Arrival Times......Page 281
5.3.6. Estimating Software Reliability......Page 293
5.4.1. Nonhomogeneous Poisson Process......Page 295