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Probability and Random Processes for Electrical and Computer Engineers


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Table of Contents

Part I: Probability and Random Variables


The Analysis of Random Experiments

Probability in Electrical and Computer Engineering

Outline of the Book

The Probability Model

The Algebra of Events

Probability of Events

Some Applications

Conditional Probability and Bayes' Rule

More Applications

Random Variables and Transformations

Discrete Random Variables

Some Common Discrete Probability Distributions

Continuous Random Variable

Some Common Continuous Probability Density Functions

CDF and PDF for Discrete and Mixed Random Variables

Transformation of Random Variables

Distributions Conditioned on an Event


Expectation, Moments, and Generating Functions

Expectation of a Random Variable

Moments of a Distribution

Generating Functions

Application: Entropy and Source Coding

Two and More Random Variables

Two Discrete Random Variables

Two Continuous Random Variables

Expectation and Correlation

Gaussian Random Variables

Multiple Random Variables

Sums of Some Common Random Variables


Inequalities, Limit Theorems, and Parameter Estimation


Convergence and Limit Theorems

Estimation of Parameters

Maximum Likelihood Estimation

Point Estimates and Confidence Intervals

Application to Signal Estimation


Random Vectors

Random Vectors

Analysis of Random Vectors


Cross Correlation and Covariance

Applications to Signal Processing


Part II: Introduction to Random Processes

Random Processes


Characterizing a Random Process

Some Discrete Random Processes

Some Continuous Random Processes


Random Signals in the Time Domain

First and Second Moments of a Random Process

Cross Correlation

Complex Random Processes

Discrete Random Processes

Transformation by Linear Systems

Some Applications


Random Signals in the Frequency Domain

Power Spectral Density Function

White Noise

Transformation by Linear Systems

Discrete Random Signals



Markov, Poisson, and Queueing Processes

The Poisson Model

Discrete-Time Markov Chains

Continuous-Time Markov Chains

Basic Queueing Theory



A Basic Combinatorics

B The Unit Impulse

C The Error Function

D Noise Sources

About the Author

Charles W. Therrien was born in Pittsfield, Massachusetts. He received both undergraduate and graduate (MS, Ph.D) degrees in electrical engineering from MIT. He was a member of the technical staff at Lincoln Laboratory from 1971 to 1984 and then moved to the Naval Postgraduate School in Monterey, California. During his more than 20 years there, he taught courses in systems and signal processing and authored three books, as well as numerous papers, in these areas. Murali Tummala is a professor in the department of electrical and computer engineering in the Graduate School of Engineering and Applied Sciences at the Naval Postgraduate School in Monterey, California. Since 1986, he has taught and conducted research there in the areas of computer networks and signal processing systems. He received his Ph.D from India Institute of Technology, Bombay in 1984.

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