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.
Author(s): Alberto Leon-Garcia
Edition: The 3rd Edition
Publisher: Prentice Hall
Year: 2008
Language: English
Pages: 833
Tags: Приборостроение;Обработка сигналов;Статистические методы;
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
