Probability, Statistics, and Random Processes

This is the standard textbook for courses on probability and statistics. While helping students to develop their problem-solving skills, the author motivates students with practical applications from various areas of ECE that demonstrate the relevance of probability theory to engineering practice. Included are chapter overviews, summaries, checklists of important terms, annotated references, and a wide selection of fully worked-out real-world examples. In this edition, the Computer Methods sections have been updated and substantially enhanced and new problems have been added.

Probability Models in Electrical and Computer Engineering
Mathematical models as tools in analysis and design
Deterministic models
Probability models
Statistical regularity
Properties of relative frequency
The axiomatic approach to a theory of probability
Building a probability model
A detailed example: a packet voice transmission system
Other examples
Communication over unreliable channels
Processing of random signals
Resource sharing systems
Reliability of systems
Overview of book
Summary
Problems
Basic Concepts of Probability Theory
Specifying random experiments
The sample space
Events
Set operations
The axioms of probability
Discrete sample spaces
Continuous sample spaces
Computing probabilities using counting methods
Sampling with replacement and with ordering
Sampling without replacement and with ordering
Permutations of n distinct objects
Sampling without replacement and without ordering
Sampling with replacement and without ordering
Conditional probability
Bayes' Rule
Independence of events
Sequential experiments
Sequences of independent experiments
The binomial probability law
The multinomial probability law
The geometric probability law
Sequences of dependent experiments
A computer method for synthesizing randomness: random number generators
Summary
Problems
Random Variables
The notion of a random variable
The cumulative distribution function
The three types of random variables
The probability density function
Conditional cdf's and pdf's
Some important random variables
Discrete random variables
Continuous random variables
Functions of a random variable
The expected value of random variables
The expected value of X. The expected value of Y = g(X). Variance of X
The Markov and Chebyshev
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Probability, Statistics, and Random Processes For Electrical Engineering

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Table of Contents

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