Intuitive Probability and Random Processes Using MATLAB®

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Third Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems.\* Realistic applications from a variety of disciplines integrated throughout the text\* Plentiful, updated and more rigorous problems, including computer "challenges"\* Revised end-of-chapter exercises sets-in all, 250 exercises with answers\* New chapter on Brownian motion and related processes\* Additional sections on Matingales and Poisson process\* Solutions manual available to adopting instructors "This book is an introduction to probability and random processes that merges theory with practice. Based on the author's belief that only "hands on" experience with the material can promote intuitive understanding the approach is to motivate the need for theory using MATLAB examples, followed by theory and analysis, and finally descriptions of "real-world" examples to acquaint the reader with a wide variety of applications."--Jacket. Read more... Introduction.- Computer Simulation.- Basic Probability.- Conditional Probability.- Discrete Random Variables.- Expected Values for Discrete Random Variables.- Multiple Discrete Random Variables.- Conditional Probability Mass Functions.- Discrete N-dimensional Random Variables.- Continuous Random Variables.- Expected Values for Continuous Random Variables.- Multiple Continuous Random Variables.- Conditional Probability Density Functions.- Continuous N-dimensional Random Variables.- Probability and Moment Approximations Using Limit Theorems.- Basic Random Processes.- Wide Sense Stationary Random Processes.- Linear Systems and Wide Sense Stationary Random Processes.- Multiple Wide Sense Stationary Random Processes.- Gaussian Random Processes.- Poisson Random Processes.- Markov Chains.- Appendix A: Glossary of Symbols and Abbreviations.- Appendix B: Assorted Math Facts and Formulas.- Appendix C: Linear and Matrix Algebra.- Appendix D: Summary of Signals, Linear Transforms, and Linear Systems.- Appendix E: Answers to Selected Problems Intuitive Probability and Random Processes using MATLAB® is an introduction to probability and random processes that merges theory with practice. Based on the author’s belief that only "hands-on" experience with the material can promote intuitive understanding, the approach is to motivate the need for theory using MATLAB examples, followed by theory and analysis, and finally descriptions of "real-world" examples to acquaint the reader with a wide variety of applications. The latter is intended to answer the usual question "Why do we have to study this?" Other salient features are: *heavy reliance on computer simulation for illustration and student exercises *the incorporation of MATLAB programs and code segments *discussion of discrete random variables followed by continuous random variables to minimize confusion *summary sections at the beginning of each chapter *in-line equation explanations *warnings on common errors and pitfalls *over 750 problems designed to help the reader assimilate and extend the concepts Intuitive Probability and Random Processes using MATLAB® is intended for undergraduate and first-year graduate students in engineering. The practicing engineer as well as others having the appropriate mathematical background will also benefit from this book. About the Author Steven M. Kay is a Professor of Electrical Engineering at the University of Rhode Island and a leading expert in signal processing. He has received the Education Award "for outstanding contributions in education and in writing scholarly books and texts..." from the IEEE Signal Processing society and has been listed as among the 250 most cited researchers in the world in engineering. Title Page......Page 1 Preface......Page 5 CONTENTS......Page 8 1. Introduction......Page 16 2. Computer Simulation......Page 28 3. Basic Prob ability......Page 51 4. Conditional Probability......Page 87 5. Discrete Random Variables......Page 119 6. Expected Values for Discrete Random Variables......Page 146 7. Multiple Discrete Random Variables......Page 180 8. Condition al Probability Mass Functions......Page 227 9. Discrete N-Dimensional Random Variables......Page 259 10. Continuous Random Variables......Page 296 11. Expected Values for Continuous Random Variables......Page 354 12. Multiple Continuous RandomVariables......Page 387 13. Conditional Probability Density Functions......Page 442 14. Continuous N- Dimensional Random Variables......Page 465 15. Prob ability and MomentApproximations Using Limit Theorems......Page 492 16. Basic Random Processes......Page 522 17. Wide Sense Station ary RandomProcesses......Page 554 18. Linear Systems and Wide Sense Stationary Random Processes......Page 604 19. Multiple Wide Sense Stationary Random Processes......Page 647 20. Gaussian Random Processes......Page 678 21. Poisson Random Processes......Page 715 22. Markov Chains......Page 743 A: Glossary of Symbols and Abbrevations......Page 779 B: Assorted Math Facts and Formulas......Page 785 C: Linear and Matrix Algebra......Page 790 D: Summary of Signals , Linear Transforms, and Linear Systems......Page 796 E: Answers to Selected Problems......Page 810 INDEX......Page 824