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Probability, Statistics, and Random Processes for Electrical Engineering, Third Edition

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Probability Models in Electrical and Computer Engineering

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Probability, Statistics, and Random Processes for Electrical Engineering, Third Edition

by Alberto Leon-Garcia

Publisher: Prentice Hall

Copyright Year: 2008

Publishing Date: 2007/12/28

eText ISBN-10: 0-13-604186-8

eText ISBN-13: 978-0-13-604186-3

Print ISBN-10: 0-13-147122-8

Print ISBN-13: 978-0-13-147122-1

Course: Electrical & Electronics Engineering

Pages: 832

eTextbook $81.50

(180 day subscription)

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Table of Contents | Description

Instructor Resources | Student Resources

ABOUT THIS TITLE - TABLE OF CONTENTS

Chapter 1. Probability Models in Electrical and Computer Engineering, 1

1.1 Mathematical Models as Tools in Analysis and Design, 2

1.2 Deterministic Models, 4

1.3 Probability Models, 4

1.4 A Detailed Example: A Packet Voice Transmission System, 9

1.5 Other Examples, 11

1.6 Overview of Book, 16

Chapter 2. Basic Concepts of Probability Theory, 21

2.1 Specifying Random Experiments, 21

2.2 The Axioms of Probability, 30

*2.3 Computing Probabilities Using Counting Methods, 41

2.4 Conditional Probability, 47

2.5 Independence of Events, 53

2.6 Sequential Experiments, 59

*2.7 Synthesizing Randomness: Random Number Generators, 67

*2.8 Fine Points: Event Classes, 70

*2.9 Fine Points: Probabilities of Sequences of Events, 75

Chapter 3. Discrete Random Variables, 96

3.1 The Notion of a Random Variable, 96

3.2 Discrete Random Variables and Probability Mass Function, 99

3.3 Expected Value and Moments of Discrete Random Variable, 104

3.4 Conditional Probability Mass Function, 111

3.5 Important Discrete Random Variables, 115

3.6 Generation of Discrete Random Variables, 127

Chapter 4. One Random Variable, 141

4.1 The Cumulative Distribution Function, 141

4.2 The Probability Density Function, 148

4.3 The Expected Value of X, 155

4.4 Important Continuous Random Variables, 163

4.5 Functions of a Random Variable, 174

4.6 The Markov and Chebyshev Inequalities, 181

4.7 Transform Methods, 184

4.8 Basic Reliability Calculations, 189

4.9 Computer Methods for Generating Random Variables, 194

*4.10 Entropy, 202

Chapter 5. Pairs of Random Variables, 233

5.1 Two Random Variables, 233

5.2 Pairs of Discrete Random Variables, 236

5.3 The Joint cdf of X and Y, 242

5.4 The Joint pdf of Two Continuous Random Variables, 248

5.5 Independence of Two Random Variables, 254

5.6 Joint Moments and Expected Values of a Function of Two Random Variables, 257

5.7 Conditional Probability and Conditional Expectation, 261

5.8 Functions of Two Random Variables, 271

5.9 Pairs of Jointly Gaussian Random Variables, 278

5.10 Generating Independent Gaussian Random Variables, 284

Chapter 6. Vector Random Variables, 303

6.1 Vector Random Variables, 303

6.2 Functions of Several Random Variables, 309

6.3 Expected Values of Vector Random Variables, 318

6.4 Jointly Gaussian Random Vectors, 325

6.5 Estimation of Random Variables, 332

6.6 Generating Correlated Vector Random Variables, 342

Chapter 7. Sums of Random Variables and Long-Term Averages, 359

7.1 Sums of Random Variables, 360

7.2 The Sample Mean and the Laws of Large Numbers, 365

Weak Law of Large Numbers, 367

Strong Law of Large Numbers, 368

7.3 The Central Limit Theorem, 369

Central Limit Theorem, 370

*7.4 Convergence of Sequences of Random Variables, 378

*7.5 Long-Term Arrival Rates and Associated Averages, 387

7.6 Calculating Distribution’s Using the Discrete Fourier Transform, 392

Chapter 8. Statistics, 411

8.1 Samples and Sampling Distributions, 411

8.2 Parameter Estimation, 415

8.3 Maximum Likelihood Estimation, 419

8.4 Confidence Intervals, 430

8.5 Hypothesis Testing, 441

8.6 Bayesian Decision Methods, 455

8.7 Testing the Fit of a Distribution to Data, 462

Chapter 9. Random Processes, 487

9.1 Definition of a Random Process, 488

9.2 Specifying a Random Process, 491

9.3 Discrete-Time Processes: Sum Process, Binomial Counting Process, and Random Walk, 498

9.4 Poisson and Associated Random Processes, 507

9.5 Gaussian Random Processes, Wiener Process and Brownian Motion, 514

9.6 Stationary Random Processes, 518

9.7 Continuity, Derivatives, and Integrals of Random Processes, 529

9.8 Time Averages of Random Processes and Ergodic Theorems, 540

*9.9 Fourier Series and Karhunen-Loeve Expansion, 544

9.10 Generating Random Processes, 550

Chapter 10. Analysis and Processing of Random Signals, 577

10.1 Power Spectral Density, 577

10.2 Response of Linear Systems to Random Signals, 587

10.3 Bandlimited Random Processes, 597

10.4 Optimum Linear Systems, 605

*10.5 The Kalman Filter, 617

*10.6 Estimating the Power Spectral Density, 622

10.7 Numerical Techniques for Processing Random Signals, 628

Chapter 11. Markov Chains, 647

11.1 Markov Processes, 647

11.2 Discrete-Time Markov Chains, 650

11.3 Classes of States, Recurrence Properties, and Limiting Probabilities, 660

11.4 Continuous-Time Markov Chains, 673

*11.5 Time-Reversed Markov Chains, 686

11.6 Numerical Techniques for Markov Chains, 692

Chapter 12. Introduction to Queueing Theory, 713

12.1 The Elements of a Queueing System, 714

12.2 Little’s Formula, 715

12.3 The M/M/1 Queue, 718

12.4 Multi-Server Systems: M/M/c, M/M/c/c, And M/M/∞, 727

12.5 Finite-Source Queueing Systems, 734

12.6 M/G/1 Queueing Systems, 738

12.7 M/G/1 Analysis Using Embedded Markov Chains, 745

12.8 Burke’s Theorem: Departures From M/M/c Systems, 754

12.9 Networks of Queues: Jackson’s Theorem, 758

12.10 Simulation and Data Analysis of Queueing Systems, 771

Appendices, 797

Appendix A. Mathematical Tables, 797

Appendix B. Tables of Fourier Transforms, 800

Appendix C. Matrices and Linear Algebra, 802

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ABOUT THIS TITLE - DESCRIPTION

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.

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