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本帖最后由 eecsseudl 于 2013-4-29 09:56 编辑
Intuitive Probability and Random Processes Using MATLAB_2006
书非常清晰，有180多M，但不是扫描版，不喜勿下！！！
目录：
Contents
Preface vii
Introduction 1
1.1 What Is Probability? 1
1.2 Types of Probability Problems 3
1.3 Probabilistic Modeling 4
1.4 Analysis versus Computer Simulation 7
1.5 Some Notes to the Reader 8
References 9
Problems 10
Computer Simulation 13
2.1 Introduction 13
2.2 Summary 13
2.3 Why Use Computer Simulation? 14
2.4 Computer Simulation of Random Phenomena 17
2.5 Determining Characteristics of Random Variables 18
2.6 Real-World Example - Digital Communications 24
References 26
Problems 26
2A Brief Introduction to MATLAB 31
Basic Probability 37
3.1 Introduction 37
3.2 Summary 37
3.3 Review of Set Theory 38
3.4 Assigning and Determining Probabilities 43
3.5 Properties of the Probability Function 48
3.6 Probabilities for Continuous Sample Spaces 52
3.7 Probabilities for Finite Sample Spaces - Equally Likely Outcomes . 54
3.8 Combinatorics 55
3.9 Binomial Probability Law 62
xii CONTENTS
3.10 Real-World Example - Quality Control 64
References 66
Problems 66
4 Conditional Probability 73
4.1 Introduction 73
4.2 Summary 73
4.3 Joint Events and the Conditional Probability 74
4.4 Statistically Independent Events 83
4.5 Bayes' Theorem 86
4.6 Multiple Experiments 89
4.7 Real-World Example - Cluster Recognition 97
References 100
Problems 100
5 Discrete Random Variables 105
5.1 Introduction 105
5.2 Summary 105
5.3 Definition of Discrete Random Variable 106
5.4 Probability of Discrete Random Variables 108
5.5 Important Probability Mass Functions Ill
5.6 Approximation of Binomial PMF by Poisson PMF 113
5.7 Transformation of Discrete Random Variables 115
5.8 Cumulative Distribution Function 117
5.9 Computer Simulation 122
5.10 Real-World Example - Servicing Customers 124
References 128
Problems 128
6 Expected Values for Discrete Random Variables 133
6.1 Introduction 133
6.2 Summary 133
6.3 Determining Averages from the PMF 134
6.4 Expected Values of Some Important Random Variables 137
6.5 Expected Value for a Function of a Random Variable 140
6.6 Variance and Moments of a Random Variable 143
6.7 Characteristic Functions 147
6.8 Estimating Means and Variances 153
6.9 Real-World Example - Data Compression 155
References 157
Problems 158
6A Derivation of E[g{X)] Formula 163
6B MATLAB Code Used to Estimate Mean and Variance 165
CONTENTS xiii
7 Multiple Discrete Random Variables 167
7.1 Introduction 167
7.2 Summary 168
7.3 Jointly Distributed Random Variables 169
7.4 Marginal PMFs and CDFs 174
7.5 Independence of Multiple Random Variables 178
7.6 Transformations of Multiple Random Variables 181
7.7 Expected Values 186
7.8 Joint Moments 189
7.9 Prediction of a Random Variable Outcome 192
7.10 Joint Characteristic Functions 198
7.11 Computer Simulation of Random Vectors 200
7.12 Real-World Example - Assessing Health Risks 202
References 204
Problems 204
7A Derivation of the Cauchy-Schwarz Inequality 213
8 Conditional Probability Mass Functions 215
8.1 Introduction 215
8.2 Summary 216
8.3 Conditional Probability Mass Function 217
8.4 Joint, Conditional, and Marginal PMFs 220
8.5 Simplifying Probability Calculations using Conditioning 225
8.6 Mean of the Conditional PMF 229
8.7 Computer Simulation Based on Conditioning 235
8.8 Real-World Example - Modeling Human Learning 237
References 240
Problems 240
9 Discrete iV-Dimensional Random Variables 247
9.1 Introduction 247
9.2 Summary 247
9.3 Random Vectors and ProbabiUty Mass Functions 248
9.4 Transformations 251
9.5 Expected Values 255
9.6 Joint Moments and the Characteristic Function 265
9.7 Conditional Probability Mass Functions 266
9.8 Computer Simulation of Random Vectors 269
9.9 Real-World Example - Image Coding 272
References 277
Problems 277
xiv CONTENTS
10 Continuous Random Variables 285
10.1 Introduction 285
10.2 Summary 286
10.3 Definition of a Continuous Random Variable 287
10.4 The PDF and Its Properties 293
10.5 Important PDFs 295
10.6 Cumulative Distribution Functions 303
10.7 Transformations 311
10.8 Mixed Random Variables 317
10.9 Computer Simulation 324
10. lOReal-World Example - Setting Clipping Levels 328
References 331
Problems 331
lOA Derivation of PDF of a Transformed Continuous Random Variable . 339
lOB MATLAB Subprograms to Compute Q and Inverse Q Functions . . . 341
11 Expected Values for Continuous Random Variables 343
11.1 Introduction 343
11.2 Summary 343
11.3 Determining the Expected Value 344
11.4 Expected Values for Important PDFs 349
11.5 Expected Value for a Function of a Random Variable 351
11.6 Variance and Moments 355
11.7 Characteristic Functions 359
11.8 Probability, Moments, and the Chebyshev Inequality 361
11.9 Estimating the Mean and Variance 363
U.lOReal-World Example-Critical Software Testing 364
References 367
Problems 367
l lA Partial Proof of Expected Value of Function of Continuous Random
Variable 375
12 Multiple Continuous Random Variables 377
12.1 Introduction 377
12.2 Summary 378
12.3 Jointly Distributed Random Variables 379
12.4 Marginal PDFs and the Joint CDF 387
12.5 Independence of Multiple Random Variables 392
12.6 Transformations 394
12.7 Expected Values 404
12.8 Joint Moments 412
12.9 Prediction of Random Variable Outcome 412
12.10 Joint Characteristic Functions 414
CONTENTS XV
12.11 Computer Simulation 415
12.12Real-World Example - Optical Character Recognition 419
References 423
Problems 423
13 Conditional Probability Density Functions 433
13.1 Introduction 433
13.2 Summary 433
13.3 Conditional PDF 434
13.4 Joint, Conditional, and Marginal PDFs 440
13.5 Simplifying Probability Calculations Using Conditioning 444
13.6 Mean of Conditional PDF 446
13.7 Computer Simulation of Jointly Continuous Random Variables . . . 447
13.8 Real-World Example - Retirement Planning 449
References 452
Problems 452
14 Continuous AT-Dimensional Random Variables 457
14.1 Introduction 457
14.2 Summary 457
14.3 Random Vectors and PDFs 458
14.4 Transformations 463
14.5 Expected Values 465
14.6 Joint Moments and the Characteristic Function 467
14.7 Conditional PDFs 471
14.8 Prediction of a Random Variable Outcome 471
14.9 Computer Simulation of Gaussian Random Vectors 475
14. lOReal-World Example - Signal Detection 476
References 479
Problems 479
15 Probability and Moment Approximations Using Limit Theorems 485
15.1 Introduction 485
15.2 Summary 486
15.3 Convergence and Approximation of a Sum 486
15.4 Law of Large Numbers 487
15.5 Central Limit Theorem 492
15.6 Real-World Example - Opinion Polling 503
References 506
Problems 507
15A MATLAB Program to Compute Repeated Convolution of PDFs . . . 511
15B Proof of Central Limit Theorem 513
xvi CONTENTS
16 Basic Random Processes 515
16.1 Introduction 515
16.2 Summary 516
16.3 What Is a Random Process? 517
16.4 Types of Random Processes 520
16.5 The Important Property of Stationarity 523
16.6 Some More Examples 528
16.7 Joint Moments 533
16.8 Real-World Example - Statistical Data Analysis 538
References 542
Problems 542
17 Wide Sense Stationary Random Processes 547
17.1 Introduction 547
17.2 Summary 548
17.3 Definition of WSS Random Process 549
17.4 Autocorrelation Sequence 552
17.5 Ergodicity and Temporal Averages 562
17.6 The Power Spectral Density 567
17.7 Estimation of the ACS and PSD 576
17.8 Continuous-Time WSS Random Processes 580
17.9 Real-World Example - Random Vibration Testing 586
References 589
Problems 590
18 Linear Systems and Wide Sense Stationary Random Processes 597
18.1 Introduction 597
18.2 Summary 598
18.3 Random Process at Output of Linear System 598
18.4 Interpretation of the PSD 607
18.5 Wiener Filtering 609
18.6 Continuous-Time Definitions and Formulas 623
18.7 Real-World Example - Speech Synthesis 626
References 630
Problems 631
18A Solution for Infinite Length Predictor 637
19 Multiple Wide Sense Stationary Random Processes 641
19.1 Introduction 641
19.2 Summary 642
19.3 Jointly Distributed WSS Random Processes 642
19.4 The Cross-Power Spectral Density 647
19.5 Transformations of Multiple Random Processes 652
CONTENTS xvii
19.6 Continuous-Time Definitions and Formulas 657
19.7 Cross-Correlation Sequence Estimation 661
19.8 Real-World Example - Brain Physiology Research 663
References 667
Problems 667
20 Gaussian Random Processes 673
20.1 Introduction 673
20.2 Summary 675
20.3 Definition of the Gaussian Random Process 676
20.4 Linear Transformations 681
20.5 Nonlinear Transformations 683
20.6 Continuous-Time Definitions and Formulas 686
20.7 Special Continuous-Time Gaussian Random Processes 689
20.8 Computer Simulation 696
20.9 Real-World Example - Estimating Fish Populations 698
References 701
Problems 702
20A MATLAB Listing for Figure 20.2 709
21 Poisson Random Processes 711
21.1 Introduction 711
21.2 Summary 713
21.3 Derivation of Poisson Counting Random Process 714
21.4 Interarrival Times 718
21.5 Arrival Times 721
21.6 Compound Poisson Random Process 723
21.7 Computer Simulation 727
21.8 Real-World Example - Automobile Traffic Signal Planning 728
References 732
Problems 732
21A Joint PDF for Interarrival Times 737
22 Markov Chains 739
22.1 Introduction 739
22.2 Summary 744
22.3 Definitions 744
22.4 Computation of State Probabilities 748
22.5 Ergodic Markov Chains 756
22.6 Further Steady-State Characteristics 759
22.7 iiT-State Markov Chains 762
22.8 Computer Simulation 764
22.9 Real-World Example - Strange Markov Chain Dynamics 765
xviii CONTENTS
References 767
Problems 767
22A Solving for the Stationary PMF 775
A Glossary of Symbols and Abbrevations 777
B Assorted Math Facts and Formulas 783
B.l Proof by Induction 783
B.2 Trigonometry 784
B.3 Limits 784
B.4 Sums 785
B.5 Calculus 786
C Linear and Matrix Algebra 789
C.l Definitions 789
C.2 Special Matrices 791
C.3 Matrix Manipulation and Formulas 792
C.4 Some Properties of PD (PSD) Matrices 793
C.5 Eigendecomposition of Matrices 793
D Summary of Signals, Linear Transforms, and Linear Systems 795
[ 本帖最后由 wodeccbp 于 2009-7-10 18:51 编辑 ]
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