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Models For Writers 12th Edition

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Description

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.

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

Readership

Professionals and students in actuarial science, engineering, operations research, and other fields in applied probability

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

Details

No. of pages:: 784

Language:: English

Copyright:: © Academic Press 2014

Published:: 22nd January 2014

Imprint:: Academic Press

eBook ISBN:: 9780124081215

Hardcover ISBN:: 9780124079489

Sheldon Ross

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.

University of Southern California, Los Angeles, USA

Reviews

'The hallmark features of this renowned text remain 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…new chapter material includes coverage of finite capacity queues, insurance risk models, and Markov chains, as well as updated data.' --Zentralblatt MATH 1284-1

'…the newest edition updated with new examples and exercises, actuarial material, Hawkes and other point processes, Brownian motion, and expanded coverage of Markov chains. Although formally rigorous, the emphasis is on helping students to develop an intuitive sense for probabilistic thinking.'--ProtoView.com, April 2014

Praise from Reviewers for the 10^th edition:
'I think Ross has done an admirable job of covering the breadth of applied probability. Ross writes fantastic problems which really force the students to think divergently...The examples, like the exercises are great.' --Matt Carlton, California Polytechnic Institute
'This is a fascinating introduction to applications from a variety of disciplines. Any curious student will love this book.' --Jean LeMaire, University of Pennsylvania
'This book may be a model in the organization of the education process. I would definitely rate this text to be the best probability models book at its level of difficulty...far more sophisticated and deliberate than its competitors.' --Kris Ostaszewski, University of Illinois

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.

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