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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:
Author Bio
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
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:
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