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
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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