Probability and Random Processes for Electrical and Computer Engineers

With updates and enhancements to the incredibly successful first edition, Probability and Random Processes for Electrical and Computer Engineers, Second Edition retains the best aspects of the original but offers an even more potent introduction to probability and random variables and processes. Written in a clear, concise style that illustrates the subject’s relevance to a wide range of areas in engineering and physical and computer sciences, this text is organized into two parts. The first focuses on the probability model, random variables and transformations, and inequalities and limit theorems. The second deals with several types of random processes and queuing theory.
New or Updated for the Second Edition:


A short new chapter on random vectors that adds some advanced new material and supports topics associated with discrete random processes


Reorganized chapters that further clarify topics such as random processes (including Markov and Poisson) and analysis in the time and frequency domain


A large collection of new MATLAB®-based problems and computer projects/assignments
Each Chapter Contains at Least Two Computer Assignments
Maintaining the simplified, intuitive style that proved effective the first time, this edition integrates corrections and improvements based on feedback from students and teachers. Focused on strengthening the reader’s grasp of underlying mathematical concepts, the book combines an abundance of practical applications, examples, and other tools to simplify unnecessarily difficult solutions to varying engineering problems in communications, signal processing, networks, and associated fields.

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.

Part I: Probability and Random Variables

Introduction
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
Applications

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
Summary

Inequalities, Limit Theorems, and Parameter Estimation
Inequalities
Convergence and Limit Theorems
Estimation of Parameters
Maximum Likelihood Estimation
Point Estimates and Confidence Intervals
Application to Signal Estimation
Summary

Random Vectors
Random Vectors
Analysis of Random Vectors
Transformations
Cross Correlation and Covariance
Applications to Signal Processing
Summary
　
Part II: Introduction to Random Processes
Random Processes
Introduction
Characterizing a Random Process
Some Discrete Random Processes
Some Continuous Random Processes
Summary

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
Summary

Random Signals in the Frequency Domain
Power Spectral Density Function
White Noise
Transformation by Linear Systems
Discrete Random Signals
Applications
Summary

Markov, Poisson, and Queueing Processes
The Poisson Model
Discrete-Time Markov Chains
Continuous-Time Markov Chains
Basic Queueing Theory
Summary

Appendices
A Basic Combinatorics
B The Unit Impulse
C The Error Function
D Noise Sources