Introduction to Probability Models, Eleventh Edition is the latest version of Sheldon Ross's classic bestseller, used extensively by professionals and as the primary text for a first undergraduate course in applied probability. The book introduces the reader to elementary probability theory and stochastic processes, and shows how probability theory can be applied fields such as engineering, computer science, management science, the physical and social sciences, and operations research.
The hallmark features of this text have been retained in this eleventh edition: superior writing style; excellent exercises and examples covering the wide breadth of coverage of probability topic; and real-world applications in engineering, science, business and economics. The 65% new chapter material includes coverage of finite capacity queues, insurance risk models, and Markov chains, as well as updated data. The book contains compulsory material for new Exam 3 of the Society of Actuaries including several sections in the new exams. It also presents new applications of probability models in biology and new material on Point Processes, including the Hawkes process. There is a list of commonly used notations and equations, along with an instructor's solutions manual.
This text will be a helpful resource for professionals and students in actuarial science, engineering, operations research, and other fields in applied probability.
Key Features
- Updated data, and a list of commonly used notations and equations, instructor's solutions manual
- Offers new applications of probability models in biology and new material on Point Processes, including the Hawkes process
- Introduces elementary probability theory and stochastic processes, and shows how probability theory can be applied in fields such as engineering, computer science, management science, the physical and social sciences, and operations research
- Covers finite capacity queues, insurance risk models, and Markov chains
- Contains compulsory material for new Exam 3 of the Society of Actuaries including several sections in the new exams
- Appropriate for a full year course, this book is written under the assumption that students are familiar with calculus
- Preface
- New to This Edition
- Course
- Examples and Exercises
- Organization
- Acknowledgments
- Introduction to Probability Theory
- Abstract
- 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
- Exercises
- References
- Random Variables
- Abstract
- 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 The Distribution of the Number of Events that Occur
- 2.8 Limit Theorems
- 2.9 Stochastic Processes
- Exercises
- References
- Conditional Probability and Conditional Expectation
- Abstract
- 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
- Markov Chains
- Abstract
- 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
- The Exponential Distribution and the Poisson Process
- Abstract
- 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
- Continuous-Time Markov Chains
- Abstract
- 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
- Renewal Theory and Its Applications
- Abstract
- 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
- Queueing Theory
- Abstract
- 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
- References
- Reliability Theory
- Abstract
- 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
- Brownian Motion and Stationary Processes
- Abstract
- 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
- Simulation
- Abstract
- 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
- 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
Ross: INTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS, 3rd Edition, 2004, (ISBN: 0125980574, $99.95) and 4th Edition, published Feb. 2009
