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Edition: 03

Copyright: 2003

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

Copyright: 2003

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

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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.

**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 MATLAB®. 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.

**Williams, Richard H. : University of New Mexico **

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

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Summary

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.

**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 MATLAB®. 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.

Author Bio

**Williams, Richard H. : University of New Mexico **

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

Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

Published: 2003

International: No

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.

**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 MATLAB®. 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.

**Williams, Richard H. : University of New Mexico **

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