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13th Edition - June 30, 2023

**Author:** Sheldon M. Ross

Paperback ISBN:

9 7 8 - 0 - 4 4 3 - 1 8 7 6 1 - 2

eBook ISBN:

9 7 8 - 0 - 4 4 3 - 1 8 7 6 0 - 5

Introduction to Probability Models: Thirteenth Edition is available in two manageable volumes: an Elementary edition appropriate for undergraduate use and an Advanced edition… Read more

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Introduction to Probability Models: Thirteenth Edition is available in two manageable volumes: an Elementary edition appropriate for undergraduate use and an Advanced edition for graduate use. Together, and through their hallmark exercises and real examples, both versions offer a comprehensive foundation of this key subject with applications across engineering, computer science, management science, the physical and social sciences and operations research. Users will find comprehensive information that introduces them to the foundations of probability modeling and stochastic processes from Random Variables, to Markov Chains and Renewal Theory.

- Awarded the 2020 Textbook Excellence Award (Texty) from the Textbook and Academic Authors Association (prior edition)
- Retains the useful organization that students and professors have relied on since 1972
- Includes new coverage on Martingales
- Offers a single source appropriate for a range of courses from undergraduate to graduate level

Undergraduate students of all backgrounds in introduction to probability modelling courses, typically in Math or Statistics departments

- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- New to This Edition
- Course
- Examples and Exercises
- Organization
- Acknowledgments
- 1: Introduction to Probability Theory
- 1.1. Introduction
- 1.2. Sample Space and Events
- 1.3. Probabilities Defined on Events
- 1.4. Conditional Probabilities
- 1.5. Independent Events
- 1.6. Bayes' Formula
- 1.7. Probability Is a Continuous Event Function
- Exercises
- References
- 2: Random Variables
- 2.1. Random Variables
- 2.2. Discrete Random Variables
- 2.3. Continuous Random Variables
- 2.4. Expectation of a Random Variable
- 2.5. Jointly Distributed Random Variables
- 2.6. Moment Generating Functions
- 2.7. Limit Theorems
- 2.8. Proof of the Strong Law of Large Numbers
- 2.9. Stochastic Processes
- Exercises
- References
- 3: Conditional Probability and Conditional Expectation
- 3.1. Introduction
- 3.2. The Discrete Case
- 3.3. The Continuous Case
- 3.4. Computing Expectations by Conditioning
- 3.5. Computing Probabilities by Conditioning
- 3.6. Some Applications
- 3.7. An Identity for Compound Random Variables
- Exercises
- 4: Markov Chains
- 4.1. Introduction
- 4.2. Chapman–Kolmogorov Equations
- 4.3. Classification of States
- 4.4. Long-Run Proportions and Limiting Probabilities
- 4.5. Some Applications
- 4.6. Mean Time Spent in Transient States
- 4.7. Branching Processes
- 4.8. Time Reversible Markov Chains
- 4.9. Markov Chain Monte Carlo Methods
- 4.10. Markov Decision Processes
- 4.11. Hidden Markov Chains
- Exercises
- References
- 5: The Exponential Distribution and the Poisson Process
- 5.1. Introduction
- 5.2. The Exponential Distribution
- 5.3. The Poisson Process
- 5.4. Generalizations of the Poisson Process
- 5.5. Random Intensity Functions and Hawkes Processes
- Exercises
- References
- 6: Continuous-Time Markov Chains
- 6.1. Introduction
- 6.2. Continuous-Time Markov Chains
- 6.3. Birth and Death Processes
- 6.4. The Transition Probability Function Pij(t)
- 6.5. Limiting Probabilities
- 6.6. Time Reversibility
- 6.7. The Reversed Chain
- 6.8. Uniformization
- 6.9. Computing the Transition Probabilities
- Exercises
- References
- 7: Renewal Theory and Its Applications
- 7.1. Introduction
- 7.2. Distribution of N(t)
- 7.3. Limit Theorems and Their Applications
- 7.4. Renewal Reward Processes
- 7.5. Regenerative Processes
- 7.6. Semi-Markov Processes
- 7.7. The Inspection Paradox
- 7.8. Computing the Renewal Function
- 7.9. Applications to Patterns
- 7.10. The Insurance Ruin Problem
- Exercises
- References
- 8: Queueing Theory
- 8.1. Introduction
- 8.2. Preliminaries
- 8.3. Exponential Models
- 8.4. Network of Queues
- 8.5. The System M/G/1
- 8.6. Variations on the M/G/1
- 8.7. The Model G/M/1
- 8.8. A Finite Source Model
- 8.9. Multiserver Queues
- Exercises
- 9: Reliability Theory
- 9.1. Introduction
- 9.2. Structure Functions
- 9.3. Reliability of Systems of Independent Components
- 9.4. Bounds on the Reliability Function
- 9.5. System Life as a Function of Component Lives
- 9.6. Expected System Lifetime
- 9.7. Systems with Repair
- Exercises
- References
- 10: Brownian Motion and Stationary Processes
- 10.1. Brownian Motion
- 10.2. Hitting Times, Maximum Variable, and the Gambler's Ruin Problem
- 10.3. Variations on Brownian Motion
- 10.4. Pricing Stock Options
- 10.5. The Maximum of Brownian Motion with Drift
- 10.6. White Noise
- 10.7. Gaussian Processes
- 10.8. Stationary and Weakly Stationary Processes
- 10.9. Harmonic Analysis of Weakly Stationary Processes
- Exercises
- References
- 11: Simulation
- 11.1. Introduction
- 11.2. General Techniques for Simulating Continuous Random Variables
- 11.3. Special Techniques for Simulating Continuous Random Variables
- 11.4. Simulating from Discrete Distributions
- 11.5. Stochastic Processes
- 11.6. Variance Reduction Techniques
- 11.7. Determining the Number of Runs
- 11.8. Generating from the Stationary Distribution of a Markov Chain
- Exercises
- References
- 12: Coupling
- 12.1. A Brief Introduction
- 12.2. Coupling and Stochastic Order Relations
- 12.3. Stochastic Ordering of Stochastic Processes
- 12.4. Maximum Couplings, Total Variation Distance, and the Coupling Identity
- 12.5. Applications of the Coupling Identity
- 12.6. Coupling and Stochastic Optimization
- 12.7. Chen–Stein Poisson Approximation Bounds
- Exercises
- 13: Martingales
- 13.1. Introduction
- 13.2. The Martingale Stopping Theorem
- 13.3. Applications of the Martingale Stopping Theorem
- 13.4. Submartingales
- Exercises
- Solutions to Starred Exercises
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- Chapter 8
- Chapter 9
- Chapter 10
- Chapter 11
- Index

- No. of pages: 870
- Language: English
- Published: June 30, 2023
- Imprint: Academic Press
- Paperback ISBN: 9780443187612
- eBook ISBN: 9780443187605

SR

Dr. Sheldon M. Ross is a professor in the Department of Industrial and Systems Engineering at the University of Southern California. He received his PhD in statistics at Stanford University in 1968. He has published many technical articles and textbooks in the areas of statistics and applied probability. Among his texts are A First Course in Probability, Introduction to Probability Models, Stochastic Processes, and Introductory Statistics. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences. He is a Fellow of the Institute of Mathematical Statistics, a Fellow of INFORMS, and a recipient of the Humboldt US Senior Scientist Award.

Affiliations and expertise

Professor, Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, USA