# Probability and Random Processes

## 2nd Edition

**With Applications to Signal Processing and Communications**

- Print ISBN 9780123869814
- Electronic ISBN 9780123870131

**With Applications to Signal Processing and Communications**

- Print ISBN 9780123869814
- Electronic ISBN 9780123870131

Miller and Childers have focused on creating a clear presentation of foundational concepts with specific applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course. It is aimed at graduate students as well as practicing engineers, and includes unique chapters on narrowband random processes and simulation techniques.
The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. **Probability and Random Processes** also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields.

* Exceptional exposition and numerous worked out problems make the book extremely readable and accessible
* The authors connect the applications discussed in class to the textbook
* The new edition contains more real world signal processing and communications applications
* Includes an entire chapter devoted to simulation techniques

Graduate-level courses in the topic with secondary interest to professionals.

Preface

CHAPTER 1. Introduction

1.1 A Speech Recognition System

1.2 A Radar System

1.3 A Communication Network

CHAPTER 2. Introduction to Probability Theory

2.1 Experiments, Sample Spaces, and Events

2.2 Axioms of Probability

2.3 Assigning Probabilities

2.4 Joint and Conditional Probabilities

2.5 Basic Combinatorics

2.6 Bayes’s Theorem

2.7 Independence

2.8 Discrete Random Variables

2.9 Engineering Application—An Optical Communication System

CHAPTER 3. Random Variables, Distributions, and Density Functions

3.1 The Cumulative Distribution Function

3.2 The Probability Density Function

3.3 The Gaussian Random Variable

3.4 Other Important Random Variables

3.5 Conditional Distribution and Density Functions

3.6 Engineering Application: Reliability and Failure Rates

CHAPTER 4. Operations on a Single Random Variable

4.1 Expected Value of a Random Variable

4.2 Expected Values of Functions of Random Variables

4.3 Moments

4.4 Central Moments

4.5 Conditional Expected Values

4.6 Transformations of Random Variables

4.7 Characteristic Functions

4.8 Probability-Generating Functions

4.9 Moment-Generating Functions

4.10 Evaluating Tail Probabilities

4.11 Engineering Application—Scalar Quantization

4.12 Engineering Application—Entropy and Source Coding

CHAPTER 5. Pairs of Random Variables

5.1 Joint Cumulative Distribution Functions

5.2 Joint Probability Density Functions

5.3 Joint Probability Mass Functions

5.4 Conditional Distribution, Density, and Mass Functions

5.5 Expected Values Involving Pairs of Random Variables

5.6 Independent Random Variables

5.7 Jointly Gaussian Random Variables

5.8 Joint Characteristic and Related Functions

5.9 Transformations o

- No. of pages:
- 522

- Language:
- English

- Copyright:
- © 2012

- Published:
- 11th January 2012

- Imprint:
- Academic Press

- Print ISBN:
- 9780123869814

- Electronic ISBN:
- 9780123870131

"...a utilitarian toolkit, to help the reader learn how to solve problems, while skirting technical issues such as measure theory…fills a particular niche in the literature, and is certainly recommended by me."--**MathSciNet, Probability and Random Processes, Second Edition**

"...primarily focused toward undergraduate students in areas of electrical and computer engineering...the book is very well written and wasy to read and follow."

-Ali Esmaili, in TECHNOMETRICS, VOL. 47, 2005

"...very well written...I think this is a highly valuable textbook that is very recommendable for students, researchers as well as practitioners interested in signal processing and communications."

- Stefan Reh, Carnegie Mellon University

"...it is well written, providing the intended readership with tools and methods to study and solve problems concerning random signals and systems."

-Evelyn Buckwar, Zentralblatt MATH Berlin

*"Electrical and computer engineers Miller (Texas A&M U.) and Childers (emeritus, U. of Florida) present a textbook for an upper-division undergraduate course in probability, or an introductory graduate course in random processes within an electrical engineering curriculum. Students are assumed to have the background appropriate to those levels. The area is primarily mathematical, but they treat the mathematics as a tool for engineers rather than a rigorous or elegant entity in its own right. They seek a balance between explaining elementary concepts clearly and providing enough depth that students can study modern communications systems, control systems, signal processing techniques, and other applications."--***Reference and Research Book News, Inc.**