Probability, Statistics, and Random Processes For Electrical Engineering, 3rd edition

Published by Pearson (December 28, 2007) © 2008
Alberto Leon-Garcia

Title overview

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.

  • Chapter overviews: brief introduction outlining chapter coverage and learning objectives.
  • Chapter summaries: concise, easy-reference sections providing quick overviews of each chapter's major topics.
  • Checklist of important terms.
  • Annotated references: suggestions of timely resources for additional coverage of critical material.
  • Numerous examples: a wide selection of fully worked-out real-world examples.
  • Computer Methods sections have been updated and substantially enhanced

 

  • New problems have been added

 

Table of contents

1. Probability Models in Electrical and Computer Engineering

  • 1.1 Mathematical Models as Tools in Analysis and Design
  • 1.2 Deterministic Models
  • 1.3 Probability Models
  • 1.4 A Detailed Example: A Packet Voice Transmission System
  • 1.5 Other Examples
  • 1.6 Overview of Book
  • Summary
  • Problems

2. Basic Concepts of Probability Theory

  • 2.1 Specifying Random Experiments
  • 2.2 The Axioms of Probability
  • 2.3 Computing Probabilities Using Counting Methods
  • 2.4 Conditional Probability
  • 2.5 Independence of Events
  • 2.6 Sequential Experiments
  • 2.7 Synthesizing Randomness: Random Number Generators
  • 2.8 Fine Points: Event Classes
  • 2.9 Fine Points: Probabilities of Sequences of Events
  • Summary
  • Problems

3. Discrete Random Variables

  • 3.1 The Notion of a Random Variable
  • 3.2 Discrete Random Variables and Probability Mass Function
  • 3.3 Expected Value and Moments of Discrete Random Variable
  • 3.4 Conditional Probability Mass Function
  • 3.5 Important Discrete Random Variables
  • 3.6 Generation of Discrete Random Variables
  • Summary
  • Problems

4. One Random Variable

  • 4.1 The Cumulative Distribution Function
  • 4.2 The Probability Density Function
  • 4.3 The Expected Value of X
  • 4.4 Important Continuous Random Variables
  • 4.5 Functions of a Random Variable
  • 4.6 The Markov and Chebyshev Inequalities
  • 4.7 Transform Methods
  • 4.8 Basic Reliability Calculations
  • 4.9 Computer Methods for Generating Random Variables
  • 4.10 Entropy
  • Summary
  • Problems

5. Pairs of Random Variables

  • 5.1 Two Random Variables
  • 5.2 Pairs of Discrete Random Variables
  • 5.3 The Joint cdf of X and Y
  • 5.4 The Joint pdf of Two Continuous Random Variables
  • 5.5 Independence of Two Random Variables
  • 5.6 Joint Moments and Expected Values of a Function of Two Random Variables
  • 5.7 Conditional Probability and Conditional Expectation
  • 5.8 Functions of Two Random Variables
  • 5.9 Pairs of Jointly Gaussian Random Variables
  • 5.10 Generating Independent Gaussian Random Variables
  • Summary
  • Problems

6. Vector Random Variables

  • 6.1 Vector Random Variables
  • 6.2 Functions of Several Random Variables
  • 6.3 Expected Values of Vector Random Variables
  • 6.4 Jointly Gaussian Random Vectors
  • 6.5 Estimation of Random Variables
  • 6.6 Generating Correlated Vector Random Variables
  • Summary
  • Problems

7. Sums of Random Variables and Long-Term Averages

  • 7.1 Sums of Random Variables
  • 7.2 The Sample Mean and the Laws of Large Numbers
  • Weak Law of Large Numbers
  • Strong Law of Large Numbers
  • 7.3 The Central Limit Theorem
  • Central Limit Theorem
  • 7.4 Convergence of Sequences of Random Variables
  • 7.5 Long-Term Arrival Rates and Associated Averages
  • 7.6 Calculating Distribution’s Using the Discrete Fourier Transform
  • Summary
  • Problems

8. Statistics

  • 8.1 Samples and Sampling Distributions
  • 8.2 Parameter Estimation
  • 8.3 Maximum Likelihood Estimation
  • 8.4 Confidence Intervals
  • 8.5 Hypothesis Testing
  • 8.6 Bayesian Decision Methods
  • 8.7 Testing the Fit of a Distribution to Data
  • Summary
  • Problems

9. Random Processes

  • 9.1 Definition of a Random Process
  • 9.2 Specifying a Random Process
  • 9.3 Discrete-Time Processes: Sum Process, Binomial Counting Process, and Random Walk
  • 9.4 Poisson and Associated Random Processes
  • 9.5 Gaussian Random Processes,Wiener Process and Brownian Motion
  • 9.6 Stationary Random Processes
  • 9.7 Continuity, Derivatives, and Integrals of Random Processes
  • 9.8 Time Averages of Random Processes and Ergodic Theorems
  • 9.9 Fourier Series and Karhunen-Loeve Expansion
  • 9.10 Generating Random Processes
  • Summary
  • Problems

10. Analysis and Processing of Random Signals

  • 10.1 Power Spectral Density
  • 10.2 Response of Linear Systems to Random Signals
  • 10.3 Bandlimited Random Processes
  • 10.4 Optimum Linear Systems
  • 10.5 The Kalman Filter
  • 10.6 Estimating the Power Spectral Density
  • 10.7 Numerical Techniques for Processing Random Signals
  • Summary
  • Problems

11. Markov Chains

  • 11.1 Markov Processes
  • 11.2 Discrete-Time Markov Chains
  • 11.3 Classes of States, Recurrence Properties, and Limiting Probabilities
  • 11.4 Continuous-Time Markov Chains
  • 11.5 Time-Reversed Markov Chains
  • 11.6 Numerical Techniques for Markov Chains
  • Summary
  • Problems

12. Introduction to Queueing Theory

  • 12.1 The Elements of a Queueing System
  • 12.2 Little’s Formula
  • 12.3 The M/M/1 Queue
  • 12.4 Multi-Server Systems: M/M/c, M/M/c/c,And
  • 12.5 Finite-Source Queueing Systems
  • 12.6 M/G/1 Queueing Systems
  • 12.7 M/G/1 Analysis Using Embedded Markov Chains
  • 12.8 Burke’s Theorem: Departures From M/M/c Systems
  • 12.9 Networks of Queues: Jackson’s Theorem
  • 12.10 Simulation and Data Analysis of Queueing Systems
  • Summary
  • Problems

Appendices

  • A. Mathematical Tables
  • B. Tables of Fourier Transforms
  • C. Matrices and Linear Algebra
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