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Introduction to probability models

Author: Sheldon M Ross
Publisher: Amsterdam ; Boston : Academic Press, ©2007.
Edition/Format:   eBook : Document : English : 9th edView all editions and formats
Summary:

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  Read more...

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ross, Sheldon M.
Introduction to probability models.
Amsterdam ; Boston : Academic Press, ©2007
(DLC) 2006051040
(OCoLC)71552484
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sheldon M Ross
ISBN: 9780080467825 0080467822 9780125980623 0125980620 9780123736352 0123736358 9786610747030 6610747032
OCLC Number: 123417622
Description: 1 online resource (xviii, 782 pages) : illustrations
Contents: Cover --
Title page --
Copyright page --
Contents --
Preface --
Chapter 1. Introduction to Probability Theory --
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 --
Chapter 2. Random Variables --
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. Limit Theorems --
2.8. Stochastic Processes --
Exercises --
References --
Chapter 3. Conditional Probability and Conditional Expectation --
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 --
Chapter 4. Markov Chains --
4.1. Introduction --
4.2. Chapman-Kolmogorov Equations --
4.3. Classification of States --
4.4. 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 --
Chapter 5. The Exponential Distribution and the Poisson Process --
5.1. Introduction --
5.2. The Exponential Distribution --
5.3. The Poisson Process --
5.4. Generalizations of the Poisson Process --
Exercises --
References --
Chapter 6. Continuous-Time Markov Chains --
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. Uniformization --
6.8. Computing the Transition Probabilities --
Exercises --
References --
Chapter 7. Renewal Theory and Its Applications --
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 --
Chapter 8. Queueing Theory --
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 --
Chapter 9. Reliability Theory --
9.1. Introduction --
9.2. Structur.
Responsibility: Sheldon M. Ross.
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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 Read more...

 
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