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.

### Table of Contents

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.