# Introduction to Probability Models

## Ross, Sheldon M.

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Ross' classic bestseller, "Introduction to Probability Models", has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It 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. 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 Hidden 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. It is a simplified approach for analyzing Nonhomogeneous Poisson processes. 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. There are also many new examples and exercises.

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Praise from Reviewers: This is a fascinating introduction to applications from a variety of disciplines. Any curious student will love this book." - Jean LeMaire, University of Pennsylvania 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, Cal Polytechnic Institute 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

Sheldon M. Ross is a professor in the Department of Industrial Engineering and Operations Research at the University of Southern California. He received his Ph.D. 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, and a recipient of the Humboldt US Senior Scientist Award.

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## 1.Introduction to Probability Models, Ninth Edition

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