Intuitive Probability and Random Processes using MATLAB

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.

Table of Contents

1 Introduction

2 Computer Simulation

3 Basic Probability

4 Conditional Probability

5 Discrete Random Variables

6 Expected Values for Discrete Random Variables

7 Multiple Discrete Random Variables

8 Conditional Probability Mass Functions

9 Discrete N-Dimensional Random Variables

10 Continuous Random Variables

11 Expected Values for Continuous Random Variables

12 Multiple Continuous Random Variables

13 Conditional Probability Density Functions

14 Continuous N-Dimensional Random Variables

15 Probability and Moment Approximations Using Limit Theorems

16 Basic Random Processes

17 Wide Sense Stationary Random Processes

18 Linear Systems and Wide Sense Stationary Random Processes

19 Multiple Wide Sense Stationary Random Processes

20 Gaussian Random Processes

21 Poisson Random Processes

22 Markov Chains

Appendix A Glossary of Symbols and Abbrevations

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

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.