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

this Is The Standard Textbook For Courses On Probability And Statistics, Not Substantially Updated. 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. booknews designed To Allow The Instructor Maximum Flexibility In The Selection Of Topics, This Textbook Covers Not Only The Standard Topics Taught In Introductory Courses On Probability, Random Variables, And Random Processes, But Also Includes Sections On Modeling, Basic Statistical Techniques, Computer Simulation, Reliability, And Entropy, As Well As Concise But Relatively Complete Introductions To Markov Chains And Queueing Theory. Annotation C. Book News, Inc., Portland, Or (booknews.com) Cover......Page 1 Title Page......Page 2 Copyright......Page 3 Contents......Page 6 Preface......Page 10 CHAPTER 1 Probability Models in Electrical and Computer Engineering......Page 16 1.1 Mathematical Models as Tools in Analysis and Design......Page 17 1.3 Probability Models......Page 19 1.4 A Detailed Example: A Packet Voice Transmission System......Page 24 1.5 Other Examples......Page 26 1.6 Overview of Book......Page 31 Summary......Page 32 Problems......Page 33 2.1 Specifying Random Experiments......Page 36 2.2 The Axioms of Probability......Page 45 2.3 Computing Probabilities Using Counting Methods......Page 56 2.4 Conditional Probability......Page 62 2.5 Independence of Events......Page 68 2.6 Sequential Experiments......Page 74 2.7 Synthesizing Randomness: Random Number Generators......Page 82 2.8 Fine Points: Event Classes......Page 85 2.9 Fine Points: Probabilities of Sequences of Events......Page 90 Summary......Page 94 Problems......Page 96 3.1 The Notion of a Random Variable......Page 111 3.2 Discrete Random Variables and Probability Mass Function......Page 114 3.3 Expected Value and Moments of Discrete Random Variable......Page 119 3.4 Conditional Probability Mass Function......Page 126 3.5 Important Discrete Random Variables......Page 130 3.6 Generation of Discrete Random Variables......Page 142 Summary......Page 144 Problems......Page 145 4.1 The Cumulative Distribution Function......Page 156 4.2 The Probability Density Function......Page 163 4.3 The Expected Value of X......Page 170 4.4 Important Continuous Random Variables......Page 178 4.5 Functions of a Random Variable......Page 189 4.6 The Markov and Chebyshev Inequalities......Page 196 4.7 Transform Methods......Page 199 4.8 Basic Reliability Calculations......Page 204 4.9 Computer Methods for Generating Random Variables......Page 209 4.10 Entropy......Page 217 Summary......Page 228 Problems......Page 230 5.1 Two Random Variables......Page 248 5.2 Pairs of Discrete Random Variables......Page 251 5.3 The Joint cdf of X and Y......Page 257 5.4 The Joint pdf of Two Continuous Random Variables......Page 263 5.5 Independence of Two Random Variables......Page 269 5.6 Joint Moments and Expected Values of a Function of Two Random Variables......Page 272 5.7 Conditional Probability and Conditional Expectation......Page 276 5.8 Functions of Two Random Variables......Page 286 5.9 Pairs of Jointly Gaussian Random Variables......Page 293 5.10 Generating Independent Gaussian Random Variables......Page 299 Summary......Page 301 Problems......Page 303 6.1 Vector Random Variables......Page 318 6.2 Functions of Several Random Variables......Page 324 6.3 Expected Values of Vector Random Variables......Page 333 6.4 Jointly Gaussian Random Vectors......Page 340 6.5 Estimation of Random Variables......Page 347 6.6 Generating Correlated Vector Random Variables......Page 357 Summary......Page 361 Problems......Page 363 CHAPTER 7 Sums of Random Variables and Long-Term Averages......Page 374 7.1 Sums of Random Variables......Page 375 7.2 The Sample Mean and the Laws of Large Numbers......Page 380 Weak Law of Large Numbers......Page 382 Strong Law of Large Numbers......Page 383 7.3 The Central Limit Theorem......Page 384 Central Limit Theorem......Page 385 7.4 Convergence of Sequences of Random Variables......Page 393 7.5 Long-Term Arrival Rates and Associated Averages......Page 402 7.6 Calculating Distribution’s Using the Discrete Fourier Transform......Page 407 Summary......Page 415 Problems......Page 417 8.1 Samples and Sampling Distributions......Page 426 8.2 Parameter Estimation......Page 430 8.3 Maximum Likelihood Estimation......Page 434 8.4 Confidence Intervals......Page 445 8.5 Hypothesis Testing......Page 456 8.6 Bayesian Decision Methods......Page 470 8.7 Testing the Fit of a Distribution to Data......Page 477 Summary......Page 484 Problems......Page 486 CHAPTER 9 Random Processes......Page 502 9.1 Definition of a Random Process......Page 503 9.2 Specifying a Random Process......Page 506 9.3 Discrete-Time Processes: Sum Process, Binomial Counting Process, and Random Walk......Page 513 9.4 Poisson and Associated Random Processes......Page 522 9.5 Gaussian Random Processes, Wiener Process and Brownian Motion......Page 529 9.6 Stationary Random Processes......Page 533 9.7 Continuity, Derivatives, and Integrals of Random Processes......Page 544 9.8 Time Averages of Random Processes and Ergodic Theorems......Page 555 9.9 Fourier Series and Karhunen-Loeve Expansion......Page 559 9.10 Generating Random Processes......Page 565 Summary......Page 569 Problems......Page 572 10.1 Power Spectral Density......Page 592 10.2 Response of Linear Systems to Random Signals......Page 602 10.3 Bandlimited Random Processes......Page 612 10.4 Optimum Linear Systems......Page 620 10.5 The Kalman Filter......Page 632 10.6 Estimating the Power Spectral Density......Page 637 10.7 Numerical Techniques for Processing Random Signals......Page 643 Summary......Page 648 Problems......Page 650 11.1 Markov Processes......Page 662 11.2 Discrete-Time Markov Chains......Page 665 11.3 Classes of States, Recurrence Properties, and Limiting Probabilities......Page 675 11.4 Continuous-Time Markov Chains......Page 688 11.5 Time-Reversed Markov Chains......Page 701 11.6 Numerical Techniques for Markov Chains......Page 707 Summary......Page 715 Problems......Page 717 CHAPTER 12 Introduction to Queueing Theory......Page 728 12.1 The Elements of a Queueing System......Page 729 12.2 Little’s Formula......Page 730 12.3 The M/M/1 Queue......Page 733 12.4 Multi-Server Systems: M/M/c, M/M/c/c, And M/M/∞......Page 742 12.5 Finite-Source Queueing Systems......Page 749 12.6 M/G/1 Queueing Systems......Page 753 12.7 M/G/1 Analysis Using Embedded Markov Chains......Page 760 12.8 Burke’s Theorem: Departures From M/M/c Systems......Page 769 12.9 Networks of Queues: Jackson’s Theorem......Page 773 12.10 Simulation and Data Analysis of Queueing Systems......Page 786 Summary......Page 797 Problems......Page 799 A. Mathematical Tables......Page 812 B. Tables of Fourier Transforms......Page 815 C. Matrices and Linear Algebra......Page 817 B......Page 820 C......Page 821 E......Page 822 G......Page 823 I......Page 824 M......Page 825 P......Page 827 R......Page 828 S......Page 831 V......Page 832 Z......Page 833 MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict Cover 1 Title Page 2 Copyright 3 Contents 6 Preface 10 CHAPTER 1 Probability Models in Electrical and Computer Engineering 16 1.1 Mathematical Models as Tools in Analysis and Design 17 1.2 Deterministic Models 19 1.3 Probability Models 19 1.4 A Detailed Example: A Packet Voice Transmission System 24 1.5 Other Examples 26 1.6 Overview of Book 31 Summary 32 Problems 33 CHAPTER 2 Basic Concepts of Probability Theory 36 2.1 Specifying Random Experiments 36 2.2 The Axioms of Probability 45 2.3 Computing Probabilities Using Counting Methods 56 2.4 Conditional Probability 62 2.5 Independence of Events 68 2.6 Sequential Experiments 74 2.7 Synthesizing Randomness: Random Number Generators 82 2.8 Fine Points: Event Classes 85 2.9 Fine Points: Probabilities of Sequences of Events 90 Summary 94 Problems 96 CHAPTER 3 Discrete Random Variables 111 3.1 The Notion of a Random Variable 111 3.2 Discrete Random Variables and Probability Mass Function 114 3.3 Expected Value and Moments of Discrete Random Variable 119 3.4 Conditional Probability Mass Function 126 3.5 Important Discrete Random Variables 130 3.6 Generation of Discrete Random Variables 142 Summary 144 Problems 145 CHAPTER 4 One Random Variable 156 4.1 The Cumulative Distribution Function 156 4.2 The Probability Density Function 163 4.3 The Expected Value of X 170 4.4 Important Continuous Random Variables 178 4.5 Functions of a Random Variable 189 4.6 The Markov and Chebyshev Inequalities 196 4.7 Transform Methods 199 4.8 Basic Reliability Calculations 204 4.9 Computer Methods for Generating Random Variables 209 4.10 Entropy 217 Summary 228 Problems 230 CHAPTER 5 Pairs of Random Variables 248 5.1 Two Random Variables 248 5.2 Pairs of Discrete Random Variables 251 5.3 The Joint cdf of X and Y 257 5.4 The Joint pdf of Two Continuous Random Variables 263 5.5 Independence of Two Random Variables 269 5.6 Joint Moments and Expected Values of a Function of Two Random Variables 272 5.7 Conditional Probability and Conditional Expectation 276 5.8 Functions of Two Random Variables 286 5.9 Pairs of Jointly Gaussian Random Variables 293 5.10 Generating Independent Gaussian Random Variables 299 Summary 301 Problems 303 CHAPTER 6 Vector Random Variables 318 6.1 Vector Random Variables 318 6.2 Functions of Several Random Variables 324 6.3 Expected Values of Vector Random Variables 333 6.4 Jointly Gaussian Random Vectors 340 6.5 Estimation of Random Variables 347 6.6 Generating Correlated Vector Random Variables 357 Summary 361 Problems 363 CHAPTER 7 Sums of Random Variables and Long-Term Averages 374 7.1 Sums of Random Variables 375 7.2 The Sample Mean and the Laws of Large Numbers 380 Weak Law of Large Numbers 382 Strong Law of Large Numbers 383 7.3 The Central Limit Theorem 384 Central Limit Theorem 385 7.4 Convergence of Sequences of Random Variables 393 7.5 Long-Term Arrival Rates and Associated Averages 402 7.6 Calculating Distribution’s Using the Discrete Fourier Transform 407 Summary 415 Problems 417 CHAPTER 8 Statistics 426 8.1 Samples and Sampling Distributions 426 8.2 Parameter Estimation 430 8.3 Maximum Likelihood Estimation 434 8.4 Confidence Intervals 445 8.5 Hypothesis Testing 456 8.6 Bayesian Decision Methods 470 8.7 Testing the Fit of a Distribution to Data 477 Summary 484 Problems 486 CHAPTER 9 Random Processes 502 9.1 Definition of a Random Process 503 9.2 Specifying a Random Process 506 9.3 Discrete-Time Processes: Sum Process, Binomial Counting Process, and Random Walk 513 9.4 Poisson and Associated Random Processes 522 9.5 Gaussian Random Processes, Wiener Process and Brownian Motion 529 9.6 Stationary Random Processes 533 9.7 Continuity, Derivatives, and Integrals of Random Processes 544 9.8 Time Averages of Random Processes and Ergodic Theorems 555 9.9 Fourier Series and Karhunen-Loeve Expansion 559 9.10 Generating Random Processes 565 Summary 569 Problems 572 CHAPTER 10 Analysis and Processing of Random Signals 592 10.1 Power Spectral Density 592 10.2 Response of Linear Systems to Random Signals 602 10.3 Bandlimited Random Processes 612 10.4 Optimum Linear Systems 620 10.5 The Kalman Filter 632 10.6 Estimating the Power Spectral Density 637 10.7 Numerical Techniques for Processing Random Signals 643 Summary 648 Problems 650 CHAPTER 11 Markov Chains 662 11.1 Markov Processes 662 11.2 Discrete-Time Markov Chains 665 11.3 Classes of States, Recurrence Properties, and Limiting Probabilities 675 11.4 Continuous-Time Markov Chains 688 11.5 Time-Reversed Markov Chains 701 11.6 Numerical Techniques for Markov Chains 707 Summary 715 Problems 717 CHAPTER 12 Introduction to Queueing Theory 728 12.1 The Elements of a Queueing System 729 12.2 Little’s Formula 730 12.3 The M/M/1 Queue 733 12.4 Multi-Server Systems: M/M/c, M/M/c/c, And M/M/∞ 742 12.5 Finite-Source Queueing Systems 749 12.6 M/G/1 Queueing Systems 753 12.7 M/G/1 Analysis Using Embedded Markov Chains 760 12.8 Burke’s Theorem: Departures From M/M/c Systems 769 12.9 Networks of Queues: Jackson’s Theorem 773 12.10 Simulation and Data Analysis of Queueing Systems 786 Summary 797 Problems 799 Appendices 812 A. Mathematical Tables 812 B. Tables of Fourier Transforms 815 C. Matrices and Linear Algebra 817 Index 820 A 820 B 820 C 821 D 822 E 822 F 823 G 823 H 824 I 824 J 825 K 825 L 825 M 825 N 827 O 827 P 827 Q 828 R 828 S 831 T 832 U 832 V 832 W 833 Y 833 Z 833