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Introduction to Probability Models, Ninth Edition, is the primary text for a first undergraduate course in applied probability. This updated edition of Ross's classic bestseller provides an introduction to elementary probability theory and stochastic processes, and shows 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. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries.
This book now contains a new section on compound random variables that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions; a new section on hiddden Markov chains, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely sequence of states; and a simplified approach for analyzing nonhomogeneous Poisson processes. There are also additional results on queues relating to the conditional distribution of the number found by an M/M/1 arrival who spends a time t in the system; inspection paradox for M/M/1 queues; and M/G/1 queue with server breakdown. Furthermore, the book includes new examples and exercises, along with compulsory material for new Exam 3 of the Society of Actuaries.
This book is essential reading for professionals and students in actuarial science, engineering, operations research, and other fields in applied probability.
A new section (3.7) on COMPOUND RANDOM VARIABLES, that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions.
A new section (4.11) on HIDDDEN MARKOV CHAINS, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely sequence of states.
Simplified Approach for Analyzing Nonhomogeneous Poisson processes
Additional results on queues relating to the
(a) conditional distribution of the number found by an M/M/1 arrival who spends a time t in the system,;
(b) inspection paradox for M/M/1 queues
(c) M/G/1 queue with server breakdown
Many new examples and exercises.
Professionals and students in actuarial science, engineering, operations research, and other fields in applied probability.
1. Introduction to Probability Theory;
2. Random Variables
3. Conditional Probability and Conditional Expectation
4. Markov Chains
5. The Exponential Distribution and the Poisson Process
6. Continuous-Time Markov Chains
7. Renewal Theory and Its Applications
8. Queueing Theory
9. Reliability Theory
10. Brownian Motion and Stationary Processes
Appendix: Solutions to Starred Exercises
- No. of pages:
- © Academic Press 2006
- 15th November 2006
- Academic Press
- eBook ISBN:
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.
Professor, Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, USA
Praise from Reviewers:
“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
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