Introduction to Probability Models

Academic Press, Dec 11, 2006 - Mathematics - 800 pages

Introduction to Probability Models, Tenth Edition, provides an introduction to elementary probability theory and stochastic processes. There are two approaches to the study of probability theory.

One is heuristic and nonrigorous, and attempts to develop in students an intuitive feel for the subject that enables him or her to think probabilistically. The other approach attempts a rigorous development of probability by using the tools of measure theory. The first approach is employed in this text.

The book begins by introducing basic concepts of probability theory, such as the random variable, conditional probability, and conditional expectation. This is followed by discussions of stochastic processes, including Markov chains and Poison processes. The remaining chapters cover queuing, reliability theory, Brownian motion, and simulation. Many examples are worked out throughout the text, along with exercises to be solved by students.

This book will be particularly useful to those interested in learning how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. Ideally, this text would be used in a one-year course in probability models, or a one-semester course in introductory probability theory or a course in elementary stochastic processes.

New to this Edition:

• 65% new chapter material including coverage of finite capacity queues, insurance risk models and Markov chains
• Contains compulsory material for new Exam 3 of the Society of Actuaries containing several sections in the new exams
• Updated data, and a list of commonly used notations and equations, a robust ancillary package, including a ISM, SSM, and test bank
• Includes SPSS PASW Modeler and SAS JMP software packages which are widely used in the field

Hallmark features:

• Superior writing style
• Excellent exercises and examples covering the wide breadth of coverage of probability topics
• Real-world applications in engineering, science, business and economics

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This book is great. I had two classes with Sheldon Ross at USC. He is really smart and this book is very comprehensive. Complex topics are covered very clearly.

Contents

 Chapter 3 Conditional Probability and Conditional Expectation 97 Chapter 4 Markov Chains 191 Chapter 5 The Exponential Distribution and the Poisson Process 291 Chapter 6 ContinuousTime Markov Chains 371 Chapter 7 Renewal Theory and Its Applications 421 Chapter 8 Queueing Theory 497
 Chapter 9 Reliability Theory 579 Chapter 10 Brownian Motion and Stationary Processes 631 Chapter 11 Simulation 667 Solutions to Starred Exercises 735 Index 775 Copyright

About the author (2006)

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.