Introduction to probability models / Sheldon M. Ross.

Format:

Book

Author/Creator:

Ross, Sheldon M.

Language:

English

Subjects (All):

Probabilities.

Physical Description:

1 online resource (801 p.)

Edition:

9th ed.

Place of Publication:

Amsterdam ; Boston : Academic Press, c2007.

Language Note:

English

Summary:

Ross's 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 Ac

Contents:

Front cover; Title page; Copyright page; Table of contents; Introduction to Probability Models; Contents; Preface; New to This Edition; Course; Examples and Exercises; Organization; Acknowledgments; 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; 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 Variables2.6. Moment Generating Functions; 2.7. Limit Theorems; 2.8. Stochastic Processes; Exercises; References; 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; 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 States4.7. 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; 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; 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

6.5. Limiting Probabilities6.6. Time Reversibility; 6.7. Uniformization; 6.8. Computing the Transition Probabilities; Exercises; References; 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; 8 Queueing Theory; 8.1. Introduction; 8.2. Preliminaries; 8.3. Exponential Models

8.4. Network of Queues8.5. 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; 9 Reliability Theory; 9.1. Introduction; 9.2. Structure Functions; 9.3. Reliability of Systems of Independent Components; 9.4. Bounds on the Reliability Function; 9.5. System Life as a Function of Component Lives; 9.6. Expected System Lifetime; 9.7. Systems with Repair; Exercises; References; 10 Brownian Motion and Stationary Processes; 10.1. Brownian Motion

10.2. Hitting Times, Maximum Variable, and the Gambler's Ruin Problem

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786610747030

9781280747038

128074703X

9780080467825

0080467822

OCLC:

666988662