Probability and Random Processes for Electrical Engineering 3rd Edition by Alberto Leon Garcia

[Alberto Leon Garcia]Probability and Random Processes for Electrical Engineering 3rd Edition

Book Title:  Probability and Random Processes for Electrical Engineering

Book Edition: 3rd Edition
Book Author: Alberto Leon Garcia
Translation: Nil
Book  Pages:  833
Language: English

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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

Summary 17

Problems 18

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

Summary 79

Problems 80

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

Summary 129

Problems 130

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

Summary 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

Summary 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

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 441

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 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-Love Expansion 544

9.10 Generating Random Processes 550

Summary 554

Problems 557

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

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

Summary 700

Problems 702

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 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

Summary 782

Problems 784

Appendices

• Mathematical Tables 797
• Tables of Fourier Transforms 800
•  Matrices and Linear Algebra 802

Index  805