Probability, random processes, and estimation theory for engineers:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Englewood Cliffs, N.J.
Prentice-Hall
1986
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002342767&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 430 S. |
| ISBN: | 013711706X |
Internformat
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| 300 | |a XV, 430 S. | ||
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| 650 | 4 | |a Estimation theory | |
| 650 | 4 | |a Probabilities | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0831 SS.92 |
|---|---|
| DE-BY-TUM_katkey | 495735 |
| DE-BY-TUM_location | LSB |
| DE-BY-TUM_media_number | TEMP2945037 |
| _version_ | 1821935761289641984 |
| adam_text | CONTENTS
Preface xi
1 INTRODUCTION TO PROBABILITY 1
1 1 Introduction: Why Study Probability? 1
1 2 The Different Kinds of Probability 2
1 3 Sets, Fields, and Events 5
1 4 Axiomatic Definition of Probability 9
1 5 Joint, Conditional, and Total Probabilities;
Independence 11
1 6 Bayes Theorem and Applications 16
1 7 Combinatorics 18
1 8 Bernoulli Trials 12
1 9 Asymptotic Behavior of the Binomial Law: The Poisson
Law 25
1 10 Derivation of the Poisson Probability Law 28
1 11 Summary 31
Problems 31
References 35
vii
2 RANDOM VARIABLES 37
2 1 Introduction 37
2 2 Definition of a Random Variable 38
2 3 Probability Distribution Function 47
2 4 Probability Density Function (pdf) 43
2 5 Continuous, Discrete, and Mixed Random Variables 49
2 6 The Dirac Delta Function 52
2 7 Conditional and Joint Distributions and Densities 56
28A Function of a Random Variable (FRV) 69
2 9 Solving Problems of the Type Y=g (X) 73
2 10 Solving Problems of the Type Z=g (X,Y) 81
2 11 Solving Problems of the Type V=g (X,Y), W=h (X,Y) 95
2 12 Summary 104
Problems 104
References 109
Additional Reading 110
3 AVERAGES 111
3 1 Expected Value of a Random Variable 111
3 2 Conditional Expectations 117
3 3 Moments 124
3 4 Chebyshev and Schwarz Inequalities 132
3 5 Moment-Generating Functions 136
3 6 Characteristic Functions 739
3 7 Summary 146
Problems 747
References 151
4 VECTOR RANDOM VARIABLES 152
4 1 Joint Distribution and Densities 152
4 2 Expectation Vectors and Covariance Matrices 156
4 3 Properties of Covariance Matrices 158
4 4 Simultaneous Diagonalizations of Two Covariance
Matrices 161
viii
Contents
4 5 The Multidimensional Gaussian Law 170
4 6 Characteristic Functions of Random Vectors 777
4 7 Summary 181
Problems 182
References 185
5 ESTIMATION AND DECISION THEORY I 187
5 1 Parameter Estimation 188
5 2 Estimation of Vector Means and Covariance
Matrices 192
5 3 Maximum Likelihood Parameter Estimation 195
5 4 Linear Estimation of Vector Parameters 198
5 5 Optimum Properties of Least-Squares Estimators
The Gauss-Markov Theorem 201
5 6 Estimation of Random Variables 205
5 7 Decision Theory: The Bayesian Approach 209
5 8 Summary 217
Problems 218
References 221
6 RANDOM SEQUENCES 222
6 1 Basic Concepts 222
6 2 Basic Principles of Discrete-Time Linear Systems 235
6 3 Random Sequences and Linear Systems 239
6 4 Convergence of Random Sequences 245
6 5 Laws of Large Numbers 253
6 6 Summary 257
Problems 257
References 262
7 RANDOM PROCESSES 263
7 1 Definitions 264
7 2 Some Important Random Processes 267
7 3 Linear Systems with Random Inputs 281
Contents
ix
7 4 Classification of Random Processes 285
7 5 Summary 290
Problems 290
References 295
8 MEAN-SQUARE CALCULUS 296
8 1 Continuity and Derivatives 296
8 2 Stochastic Integrals 308
8 3 Stochastic Differential Equations 311
8 4 Ergodicity 316
8 5 Karhunen-Loöve Expansion 323
8 6 Summary 327
App Integral Equations 328
Problems 332
References 336
9 STATIONARY PROCESSES AND SEQUENCES 337
9 1 Power Spectral Density 338
9 2 More on White Noise 343
9 3 Stationary Process and Linear Systems 345
9 4 WSS Random Sequences 352
9 5 Vector Processes and State Equations 354
9 6 Representation of Bandlimited and Periodic
Processes 360
9 7 Summary 367
App Residue Method for Inverse Fourier Transformation 368
Problems 374
References 379
10 ESTIMATION THEORY II 380
10 1 The Conditional Mean Revisited 380
10 2 Orthogonality and Linear Estimation 382
10 3 Innovations Sequences and Prediction 388
Contents
10 4 Kalman Predictor and Filter 393
10 5 Wiener Filters for Random Sequences 401
10 6 Linear Estimation for Random Processes 404
10 7 Summary 418
Problems 419
References 421
Index 423
Contents
|
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| id | DE-604.BV003682304 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T08:08:29Z |
| institution | BVB |
| isbn | 013711706X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002342767 |
| oclc_num | 12313123 |
| open_access_boolean | |
| owner | DE-384 DE-91 DE-BY-TUM DE-29T DE-11 |
| owner_facet | DE-384 DE-91 DE-BY-TUM DE-29T DE-11 |
| physical | XV, 430 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Prentice-Hall |
| record_format | marc |
| spellingShingle | Stark, Henry Woods, John W. Probability, random processes, and estimation theory for engineers Estimation, Théorie de l' ram Probabilités ram Processus stochastiques ram Estimation theory Probabilities Stochastic processes Signalverarbeitung (DE-588)4054947-1 gnd Statistik (DE-588)4056995-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Schätztheorie (DE-588)4121608-8 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4054947-1 (DE-588)4056995-0 (DE-588)4057630-9 (DE-588)4121608-8 (DE-588)4137007-7 (DE-588)4064324-4 |
| title | Probability, random processes, and estimation theory for engineers |
| title_auth | Probability, random processes, and estimation theory for engineers |
| title_exact_search | Probability, random processes, and estimation theory for engineers |
| title_full | Probability, random processes, and estimation theory for engineers Henry Stark ; John W. Woods |
| title_fullStr | Probability, random processes, and estimation theory for engineers Henry Stark ; John W. Woods |
| title_full_unstemmed | Probability, random processes, and estimation theory for engineers Henry Stark ; John W. Woods |
| title_short | Probability, random processes, and estimation theory for engineers |
| title_sort | probability random processes and estimation theory for engineers |
| topic | Estimation, Théorie de l' ram Probabilités ram Processus stochastiques ram Estimation theory Probabilities Stochastic processes Signalverarbeitung (DE-588)4054947-1 gnd Statistik (DE-588)4056995-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Schätztheorie (DE-588)4121608-8 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Estimation, Théorie de l' Probabilités Processus stochastiques Estimation theory Probabilities Stochastic processes Signalverarbeitung Statistik Stochastischer Prozess Schätztheorie Wahrscheinlichkeit Wahrscheinlichkeitsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002342767&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT starkhenry probabilityrandomprocessesandestimationtheoryforengineers AT woodsjohnw probabilityrandomprocessesandestimationtheoryforengineers |
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