Higher Education

# Probability, Statistics, and Random Processes for Engineers, 1st Edition

• Richard H. Williams University of New Mexico
• ISBN-10: 0534368883  |  ISBN-13: 9780534368883
• 480 Pages
• College Bookstore Wholesale Price = \$135.25

### Overview

This book focuses on teaching probabilistic and statistical methods to upper-division electrical and computer engineering (EECE) students. It is the result of over 20 years of teaching this course in the rapidly changing environment of EECE education. In addition to being a readable and focused book for EECE students, the book is a teachable book for EECE instructors with a variety of technical backgrounds. The first part of the book, Chapters 1-3, contains fundamental probability material. The second part, Chapters 4-7, presents applications and extensions based upon the first three chapters. The four application chapters may be studied in any order, as they do not depend on each other in any essential way.

### Features and Benefits

• Includes a wealth of applications for electrical and computer engineering (EECE) students.
• Introduces functions with random features, such as noise or sinusoids with random phase, in Chapter 4. The coverage is restricted to "wide-sense stationary" random processes, a class of functions which are very useful in modern practice and also supply a starting point for more complicated applications.
• Illustrates the application of probability to the reliability of devices and software in Chapter 7. The chapter focuses on failure rates (hazard functions), a description that engineers look to for guidance in a variety of cases involving system reliability.
• Contains computer simulations written in pseudocode as well as applications in MATLABĀ®. Computer exercises appear at the end of each chapter.
• Features helpful appendices such as Appendix A, a summary of probability models discussed throughout the book. Readers may refer to Appendix A rather than leaf through the various parts of the book searching for features of a probability model.

1. PROBABILITY.
Why Probability? General Outline of this Chapter. Probability Calculations. Summary. Exercises. Computer Exercises. Bibliography.
2. SINGLE RANDOM VARIABLES.
Introduction. General Outline of this Chapter. Probability Models. Expectations. Characteristic Functions. Functions of Single Random Variables. Conditioned Random Variables. Summary. Exercises. Computer Exercises.
3. MULTIPLE RANDOM VARIABLES.
Introduction. General Outline of this Chapter. Bivariate Cumulative and Density Functions. Bivariate Expectations. Bivariate Transformations. Gaussian Bivariate Random Variables. Sums of Two Independent Random Variables. Sums of IID Random Variables. Conditional Joint Probabilities. Selected Topics. Summary. Exercises. Computer Exercises.
4. RANDOM PROCESSES.
Introduction. An Ensemble. Probability Density Functions. Independence. Expectations. Stationarity. Correlation Functions. Ergodic Random Processes. Power Spectral Densities. Linear Systems. Noise. Matched Filters. Least Mean-square Filters. Summary. Exercises. Computer Exercises.
5. STATISTICAL INFERENCES AND CONFIDENCE.
Introduction. The Maximum Likelihood Technique. Estimation of Mean and Variance. Summary. Exercises. Computer Exercises.
6. RANDOM COUNTABLE EVENTS.
Introduction. Poisson Random Variables. Erlang Random Variables. Queuing. Summary. Exercises. Computer Exercises.
7. RELIABILITY.
Introduction. Reliability. Failure Rates. System Reliability. The Weibull Model. Accelerated Life Testing. Summary. Exercises. Computer Exercises.
APPENDICES.
Selected Probability Models. A Brief Review of Counting Techniques. A Uniform Random Number Generator. Normalized Gaussian Random Variables. Unit-Step and Unit-Impulse Functions. Statistics and Sample Data. A Central Limit Theorem. Tables: Chi-Square and Student's t. Wiener-Khinchin Relations.

## Efficacy and Outcomes

### Reviews

"This text contains the absolutely necessary information on probability and stochastic processes that is needed in engineering. I found no redundancy in the chapters. It is carefully written in an easy to understand language that covers all the necessary topics for an introduction to this subject area."

— Dimitrios Hatzinakos, University of Toronto

"The text provides a smooth, orderly coverage of the subject material. The student can move with ease from one section to the next. There is enough relevant and practical examples in the text to illustrate the theory."

— Salah Yousif, California State University, Sacramento

"It is well polished in presenting the abstract statistics topics."

— Ron Gallagher, University of Toledo

## Meet the Author

### Richard H. Williams

Richard H. Williams is Professor Emeritus at the University of New Mexico. Before beginning his teaching career, Professor Williams was a staff member for electronic test equipment at Sandia National Laboratories (1953-1959). He then worked as a research associate at the University of New Mexico (1959-1961). From 1961 to 1998, he was a faculty member in the Electrical and Computer Engineering (EECE) Department at the University of New Mexico. His teaching experience included Electronics, Biomedical Engineering, Digital Signal Processing, and Modern Manufacturing Methods. These subjects included probability and statistical methods.