Introduction to Probability Models PDF
Preview Introduction to Probability Models
Cover image Page: Cover Title page Page: Cover Table of Contents Page: Cover Copyright Page: Cover Preface Page: xi New to This Edition Page: xi Course Page: xii Examples and Exercises Page: xii Organization Page: xii Acknowledgments Page: xiv CHAPTER 1. Introduction to Probability Theory Page: 1 1.1 Introduction Page: 1 1.2 Sample Space and Events Page: 1 1.3 Probabilities Defined on Events Page: 4 1.4 Conditional Probabilities Page: 6 1.5 Independent Events Page: 10 1.6 Bayes′ Formula Page: 12 Exercises Page: 15 References Page: 20 CHAPTER 2. Random Variables Page: 21 2.1 Random Variables Page: 21 2.2 Discrete Random Variables Page: 25 2.2.2 The Binomial Random Variable Page: 27 2.4 Expectation of a Random Variable Page: 36 2.9 Stochastic process Page: 84 Exercises Page: 86 References Page: 95 CHAPTER 3. Conditional Probability and Conditional Expectation Page: 97 3.1 Introduction Page: 97 3.2 The Discrete Case Page: 97 3.3 The Continuous Case Page: 102 3.4 Computing Expectations by Conditioning Page: 106 3.5 Computing Probabilities by Conditioning Page: 122 3.6 Some Applications Page: 139 3.7 An Identity for Compound Random Variables Page: 166 Exercises Page: 173 CHAPTER 4. Markov Chains Page: 191 4.1 Introduction Page: 191 4.2 Chapman-Kolmogorov Equations Page: 195 4.3 Classification of States Page: 204 4.4 Limiting Probabilities Page: 214 4.5 Some Applications Page: 230 4.6 Mean Time Spent in Transient States Page: 242 4.7 Branching Processes Page: 245 4.8 Time Reversible Markov Chains Page: 249 4.9 Markov Chain Monte Carlo Methods Page: 260 4.10 Markov Decision Processes Page: 265 4.11 Hidden Markov Chains Page: 268 Exercises Page: 275 References Page: 290 CHAPTER 5. The Exponential Distribution and the Poisson Process Page: 291 5.1 Introduction Page: 291 5.2 The Exponential Distribution Page: 292 5.3 The Poisson Process Page: 312 Example 5.18 (An Infinite Server Queue) Page: 327 Example 5.19 (Minimizing the Number of Encounters) Page: 329 5.3. Proof of Proposition Page: 333 5.4 Generalizations of the Poisson Process Page: 339 Exercises Page: 354 References Page: 370 CHAPTER 6. Continuous-Time Markov Chains Page: 371 6.1 Introduction Page: 371 6.2 Continuous-Time Markov Chains Page: 372 6.3 Birth and Death Processes Page: 374 6.6 Time Reversibility Page: 397 6.7 Uniformization Page: 405 6.8 Computing the Transition Probabilities Page: 409 Exercises Page: 411 References Page: 419 CHAPTER 7. Renewal Theory and Its Applications Page: 421 7.1 Introduction Page: 421 7.2 Distribution of N(t) Page: 423 7.3 Limit Theorems and Their Applications Page: 427 7.4 Renewal Reward Processes Page: 439 7.5 Regenerative Processes Page: 447 7.6 Semi−Markov Processes Page: 457 7.7 The Inspection Paradox Page: 460 7.8 Computing the Renewal Function Page: 463 7.9 Applications to Patterns Page: 466 7.10 The Insurance Ruin Problem Page: 478 Exercises Page: 484 References Page: 495 CHAPTER 8. Queueing Theory Page: 497 8.1 Introduction Page: 497 8.2 Preliminaries Page: 498 8.3 Exponential Models Page: 502 8.4 Network of Queues Page: 527 8.5 The System M/G/1 Page: 537 8.6 Variations on the M/G/1 Page: 541 8.7 The Model G/M/1 Page: 553 8.8 A Finite Source Model Page: 558 8.9 Multiserver Queues Page: 562 References Page: 578 CHAPTER 9. Reliability Theory Page: 579 9.1 Introduction Page: 579 9.2 Structure Functions Page: 579 9.3 Reliability of Systems of Independent Components Page: 585 9.4 Bounds on the Reliability Function Page: 590 9.5 System Life as a Function of Component Lives Page: 602 9.6 Expected System Lifetime Page: 610 9.7 Systems with Repair Page: 616 Exercises Page: 623 References Page: 629 CHAPTER 10. Brownian Motion and Stationary Processes Page: 631 10.1 Brownian Motion Page: 631 10.2 Hitting Times, Maximum Variable, and the Gambler’s Ruin Problem Page: 635 10.3 Variations on Brownian Motion Page: 636 10.4 Pricing Stock Options Page: 638 10.5 White Noise Page: 649 10.6 Gaussian Processes Page: 651 10.7 Stationary and Weakly Stationary Processes Page: 654 10.8 Harmonic Analysis of Weakly Stationary Processes Page: 659 Exercises Page: 661 References Page: 665 CHAPTER 11. Simulation Page: 667 11.1 Introduction Page: 667 11.2 General Techniques for Simulating Continuous Random Variables Page: 672 11.3 Special Techniques for Simulating Continuous Random Variables Page: 680 11.4 Simulating from Discrete Distributions Page: 688 11.5 Stochastic Processes Page: 695 11.6 Variance Reduction Techniques Page: 705 11.7 Determining the Number of Runs Page: 722 11.8 Generating from the Stationary Distribution of a Markov Chain Page: 723 References Page: 734 APPENDIX. Solutions to Starred Exercises Page: 735 1 Chapter 1 Page: 735 2 Chapter 2 Page: 738 3 Chapter 3 Page: 741 4 Chapter 4 Page: 748 5 Chapter 5 Page: 751 6 Chapter 6 Page: 755 7 Chapter 7 Page: 758 8 Chapter 8 Page: 761 9 Chapter 9 Page: 767 10 Chapter 10 Page: 769 11 Chapter 11 Page: 771 Index Page: 774
Description:Introduction to Probability Models, Tenth Edition, provides an introduction to elementary probability theory and stochastic processes. There are two approaches to the study of probability theory. One is heuristic and nonrigorous, and attempts to develop in students an intuitive feel for the subject that enables him or her to think probabilistically. The other approach attempts a rigorous development of probability by using the tools of measure theory. The first approach is employed in this text.
The book begins by introducing basic concepts of probability theory, such as the random variable, conditional probability, and conditional expectation. This is followed by discussions of stochastic processes, including Markov chains and Poison processes. The remaining chapters cover queuing, reliability theory, Brownian motion, and simulation. Many examples are worked out throughout the text, along with exercises to be solved by students.
This book will be particularly useful to those interested in learning 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. Ideally, this text would be used in a one-year course in probability models, or a one-semester course in introductory probability theory or a course in elementary stochastic processes.
New to this Edition:
- 65% new chapter material including coverage of finite capacity queues, insurance risk models and Markov chains
- Contains compulsory material for new Exam 3 of the Society of Actuaries containing several sections in the new exams
- Updated data, and a list of commonly used notations and equations, a robust ancillary package, including a ISM, SSM, and test bank
- Includes SPSS PASW Modeler and SAS JMP software packages which are widely used in the field
Hallmark features:
- Superior writing style
- Excellent exercises and examples covering the wide breadth of coverage of probability topics
- Real-world applications in engineering, science, business and economics
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