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


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

Table of Contents

  • 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


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© 2014
Academic Press
Print ISBN:
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"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.", April 2014
Praise from Reviewers for the 10th 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