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Library of Congress Cataloging-in-Publication Data Leon-Garcia. Alberto Probability, statistics, and random processes for electrical engineering / Alberto Leon-Garcia--3rd ed cm Includes bibliographical references and index ISBN-13:978-0-13-147122-1(alk. paper) 1. Electric engineering--Mathematics. 2. Probabilities. 3. Stochastic processes. I Leon-Garcia, Alberto Probability and random processes for electrical engineering. II. Title TK153.L425200 51920246213-dc22 2007046492 Vice President and Editorial Director. ECS: Marcia Horton associate editor: Alice dworkin Editorial Assistant: William opaluch Senior managing Editor: Scott Disanno Production Editor: Craig little Art Director: Javen Conte Cover Designer: Bruce Kenselaar Art Editor: Greg dulles Manufacturing Manager: Alan Fischer Manufacturing Buyer: Lisa McDowell Marketing Manager Tim galligan PEARSON C 2008 Pearson education Inc Pearson Prentice hal Pre ha Upper Saddle River, NJ07458 Pearson education inc All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher Pearson Prentice Hall M is a trademark of Pearson Education Inc MATLaB is a registered trademark of The Math Works, Inc. All other product or brand names are trademarks or registered trademarks of their respective holders The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to the material contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of this material Printed in the United states of america 10987654321 工SBN口-13 71己己-凸 日7凸 彐-1471己己-1 Pearson education ltd. London Pearson Education Australia Pty Ltd, Sydney Pearson Education Singapore, Pte Ltd Pearson Education North Asia Ltd, Hong Kong Pearson Education Canada Inc. Toronto Pearson educacion de mexico. S.A. de C.v. Pearson Education -Japan, Tokyo Pearson Education Malaysia, Pte Ltd Pearson Education, Upper Saddle river, New Jersey TO KAREN. CARLOS. MARISA AND MICHAEL This page intentionally left blank Contents Preface 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 1.4 A Detailed Example: a Packet Voice Transmission System 9 1.5 Other Examples 11 1.6 Overview of book 16 Summary 17 Problems 18 CHaPTeR 2 Basic Concepts of Probability Theory 21 2.1 Specifying Random Experiments 21 2.2 The Axioms of Probability 2.3 Computing probabilities Using Counting methods 2.4 Conditional Probability 47 2.5 Independence of Events 53 2.6 Sequential Experiments 59 2.7 Synthesizing randomness random Number generators 2. 8 Fine points event classes 70 2.9 Fine Points: Probabilities of sequences of events 75 Summary 79 Problems 80 ChaPteR 3 Discrete Random variables 96 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 104 3.4 Conditional Probability mass Function 111 3.5 Important Discrete Random Variables 115 3.6 Generation of Discrete Random variables 127 Summary 129 Problems 130 vi Contents 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 20 Summar 213 Problems 215 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 S ummar 286 Problems 288 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 Summary 346 Problems 348 Contents vii 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 Summary 400 Problems 402 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 8.6 Bayesian Decision Methods 455 8.7 Testing the Fit of a Distribution to Data 462 Summary 469 Problems 471 ChaPTER 9 Random Processes 487 9.1 Definition of a random Process 488 9.2 Specifying a random process 9.3 Discrete-Time Processes: Sum Process, Binomial Counting proce 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 Summary 554 Problems 557 viii Contents CHAPTER 10 Analysis and processing of Random signals 577 10.1 Power Spectral Density 577 10.2 Response of Linear systems to random signal 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 Summary 633 Problems 635 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 Summar 700 Problems 702 CHAPTER 12 Introduction to Queueing Theory 713 12.1 The Elements of a Queueing System 714 12.2 Littles 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/oo 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: Jacksons Theorem 758 12.10 Simulation and Data Analysis of Queueing Systems 77 Summary 782 Problems 784 Appendices A. Mathematical Tables 797 B. Tables of fourier transforms 800 C. Matrices and Linear algebra 802 Index Preface This book provides a carefully motivated, accessible, and interesting introduction to probability, statistics, and random processes for electrical and computer engineers. The complexity of the systems encountered in engineering practice calls for an understand ing of probability concepts and a facility in the use of probability tools. The goal of the introductory course should therefore be to teach both the basic theoretical concepts and techniques for solving problems that arise in practice. The third edition of this book achieves this goal by retaining the proven features of previous editions o Relevance to engineering practice Clear and accessible introduction to probability Computer exercises to develop intuition for randomness arge number and variety of problems Curriculum flexibility through rich choice of topics Careful development of random process concepts This edition also introduces two major new features Introduction to statistics Extensive use of maTLaB/Octave RELEVANCE TO ENGINEERING PRACTICE Motivating students is a major challenge in introductory probability courses. Instructors need to respond by showing students the relevance of probability theory to engineering practice. Chapter 1 addresses this challenge by discussing the role of probability models n engineering design. Practical current applications from various areas of electrical and computer engineering are used to show how averages and relative frequencies provide the proper tools for handling the design of systems that involve randomness. These ap- plication areas include wireless and digital communications, digital media and signal processing, system reliability, computer networks, and Web systems. These areas are used in examples and problems throughout the text ACCESSIBLE INTRODUCTION TO PROBABILITY THEORY Probability theory is an inherently mathematical subject so concepts must be presented carefully, simply, and gradually. The axioms of probability and their corollaries are devel- oped in a clear and deliberate manner. The model-building aspect is introduced through the assignment of probability laws to discrete and continuous sample spaces. The notion of a single discrete random variable is developed in its entirety, allowing the student to 【实例截图】
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