http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
1 online resource (xi, 556 pages) : illustrations
Front Cover; Introduction to Probability Models; Copyright Page; Table of 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 ProcessesExercises; 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; 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. Branching Processes; 4.7. Time Reversible Markov Chains; 4.8. Markov Decision Processes; Exercises; References.
Chapter 5. The Exponential Distribution and the Poisson Process5.1. 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 Kolmogorov Differential Equations; 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; 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. Multiserver Queues; Exercises; References; Chapter 9. Reliability Theory; 9.1. Introduction; 9.2. Structure Functions.
9.3. Reliability of Systems of Independent Components9.4. 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; Chapter 10. Brownian Motion and Stationary Processes; 10.1. Brownian Motion; 10.2. Hitting Times, Maximum Variable, and the Gambler's Ruin Problem; 10.3. Variations on Brownian Motion; 10.4. Pricing Stock Options; 10.5. White Noise; 10.6. Gaussian Processes; 10.7. Stationary and Weakly Stationary Processes; 10.8. Harmonic Analysis of Weakly Stationary Processes; Exercises.
Includes bibliographical references and index.