Probability, random variables, and stochastic processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London u.a.
McGraw-Hill
1984
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | McGraw-Hill series in electrical engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 576 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Probability, random variables, and stochastic processes |c Athanasios Papoulis |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a London u.a. |b McGraw-Hill |c 1984 | |
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| 650 | 4 | |a Probabilités | |
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| 650 | 4 | |a Variables aléatoires | |
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| 650 | 4 | |a Probabilities | |
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| 650 | 4 | |a Stochastic processes | |
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Datensatz im Suchindex
| _version_ | 1804116764129230848 |
|---|---|
| adam_text | CONTENTS
Preface to the Second Edition xi
Preface to the First Edition xiii
Part 1 Probability and Random Variables
1 The Meaning of Probability 3
1-1 Introduction 3
1-2 The Definitions 5
1-3 Probability and Induction 12
1-4 Causality versus Randomness 13
Concluding Remarks 14
2 The Axioms of Probability 15
2-1 Set Theory 15
2-2 Probability Space 19
2-3 Conditional Probability 27
Problems 36
3 Repeated Trials 37
3-1 Combined Experiments 37
3-2 Bernoulli Trials 42
3-3 Asymptotic Theorems 46
3-4 Poisson Theorem and Random Points 54
3-5 Bayes Theorem and Statistics 59
Problems 60
4 The Concept of a Random Variable 63
4-1 Introduction 63
4-2 Distribution and Density Functions 66
vii
viii contents
4-3 Special Cases 73
4-4 Conditional Distributions 79
4-5 Total Probability and Bayes Theorem 84
Problems 88
5 Functions of One Random Variable 89
5-1 The Random Variable g(x) 89
5-2 The Distribution of g(x) 90
5-3 Mean and Variance 104
5-4 Moments 110
5-5 Characteristic Functions 115
Problems 120
6 Two Random Variables 123
6-1 Joint Statistics 123
6-2 One Function of Two Random Variables 134
6-3 Two Functions of Two Random Variables 141
Problems 147
7 Moments and Conditional Statistics 149
7-1 Joint Moments 149
7-2 Joint Characteristic Functions 155
7-3 Conditional Distributions 159
7-4 Conditional Expected Values 163
7-5 Mean Square Estimation 166
Problems 170
8 Sequences of Random Variables 172
8-1 General Concepts 172
8-2 Conditional Densities 181
8-3 Characteristic Functions and Normality 184
8-4 Random Sequences and Stochastic Convergence 188
8-5 The Central Limit Theorem 194
Problems 200
Part 2 Stochastic Processes
9 General Concepts 205
9-1 Introduction 205
9-2 Definitions 215
9-3 Stationary Processes 219
9-4 Systems with Stochastic Inputs 231
9-5 Ergodicity 245
Appendix 9A Continuity, Differentiation, Integration 255
Appendix 9B Shift Operators and Stationary Processes 257
Problems 258
CONTENTS IX
10 Spectral Analysis 263
10-1 Correlations and Spectra 263
10-2 Linear Systems 271
10-3 Hilbert Transforms, Shot Noise, Thermal Noise 283
10-4 Discrete-Time Processes 289
10-5 Factorization and Innovations 294
10-6 Spectral Representation and Fourier Transforms 301
Appendix 10A The Poisson Sum Formula 308
Appendix 10B Schwarz Inequality 309
Problems 310
11 Applications 314
11-1 Modulation 314
11-2 Bandlimited Processes and Sampling Theory 331
11-3 Normal Processes and Brownian Motion 338
11-4 The Level-Crossing Problem 345
Problems 354
Part 3 Selected Topics
12 Queueing Theory, Shot Noise, Markoff Processes 359
12-1 Poisson Points and Renewals 359
12-2 Queueing Theory 367
12-3 Shot Noise 379
12-4 Markoff Processes 385
Problems 403
13 Mean Square Estimation 407
13-1 The Orthogonality Principle 407
13-2 Stochastic Processes 414
13-3 Smoothing 418
13-4 Prediction 421
13-5 Filtering and Prediction 446
13-6 Kalman Filters 454
13-7 Adaptive Filters 467
Appendix 13A Minimum-Phase Functions 474
Appendix 13B All-Pass Functions 474
Problems 476
14 Spectral Estimation 480
14-1 Deterministic Data 480
14-2 Stochastic Data 491
Problems 498
X CONTENTS
15 Entropy 500
15-1 Introduction 500
15-2 Basic Concepts 508
15-3 Random Variables and Stochastic Processes 523
15-4 The Maximum Entropy Method 535
15-5 Coding 544
15-6 Channel Capacity 556
Problems 565
Bibliography 568
Index 570
|
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| author | Papoulis, Athanasios 1921-2002 |
| author_GND | (DE-588)132599031 |
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| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV002303116 |
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| classification_tum | MAT 600f |
| ctrlnum | (OCoLC)9757552 (DE-599)BVBBV002303116 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:41Z |
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| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001513684 |
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| publishDateSort | 1984 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | McGraw-Hill series in electrical engineering |
| spelling | Papoulis, Athanasios 1921-2002 Verfasser (DE-588)132599031 aut Probability, random variables, and stochastic processes Athanasios Papoulis 2. ed. London u.a. McGraw-Hill 1984 XV, 576 S. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in electrical engineering Probabilities - For electrical engineering Probabilités Processus stochastiques Stochastik swd Stochastische processen gtt Stochastischer Prozess swd Variables aléatoires Waarschijnlijkheidstheorie gtt Wahrscheinlichkeitsrechnung swd Zufallsvariable swd Probabilities Random variables Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Statistische Nachrichtentheorie (DE-588)4191729-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wirtschaftlichkeitsrechnung (DE-588)4066426-0 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Stochastisches Signal (DE-588)4140374-5 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Stochastik (DE-588)4121729-9 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Stochastischer Prozess (DE-588)4057630-9 s Wirtschaftlichkeitsrechnung (DE-588)4066426-0 s Zufallsvariable (DE-588)4129514-6 s 1\p DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 2\p DE-604 Statistische Nachrichtentheorie (DE-588)4191729-7 s 3\p DE-604 Stochastisches Signal (DE-588)4140374-5 s 4\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001513684&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Papoulis, Athanasios 1921-2002 Probability, random variables, and stochastic processes Probabilities - For electrical engineering Probabilités Processus stochastiques Stochastik swd Stochastische processen gtt Stochastischer Prozess swd Variables aléatoires Waarschijnlijkheidstheorie gtt Wahrscheinlichkeitsrechnung swd Zufallsvariable swd Probabilities Random variables Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd Statistische Nachrichtentheorie (DE-588)4191729-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wirtschaftlichkeitsrechnung (DE-588)4066426-0 gnd Zufallsvariable (DE-588)4129514-6 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Stochastisches Signal (DE-588)4140374-5 gnd Stochastik (DE-588)4121729-9 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4191729-7 (DE-588)4079013-7 (DE-588)4066426-0 (DE-588)4129514-6 (DE-588)4064324-4 (DE-588)4140374-5 (DE-588)4121729-9 |
| title | Probability, random variables, and stochastic processes |
| title_auth | Probability, random variables, and stochastic processes |
| title_exact_search | Probability, random variables, and stochastic processes |
| title_full | Probability, random variables, and stochastic processes Athanasios Papoulis |
| title_fullStr | Probability, random variables, and stochastic processes Athanasios Papoulis |
| title_full_unstemmed | Probability, random variables, and stochastic processes Athanasios Papoulis |
| title_short | Probability, random variables, and stochastic processes |
| title_sort | probability random variables and stochastic processes |
| topic | Probabilities - For electrical engineering Probabilités Processus stochastiques Stochastik swd Stochastische processen gtt Stochastischer Prozess swd Variables aléatoires Waarschijnlijkheidstheorie gtt Wahrscheinlichkeitsrechnung swd Zufallsvariable swd Probabilities Random variables Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd Statistische Nachrichtentheorie (DE-588)4191729-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wirtschaftlichkeitsrechnung (DE-588)4066426-0 gnd Zufallsvariable (DE-588)4129514-6 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Stochastisches Signal (DE-588)4140374-5 gnd Stochastik (DE-588)4121729-9 gnd |
| topic_facet | Probabilities - For electrical engineering Probabilités Processus stochastiques Stochastik Stochastische processen Stochastischer Prozess Variables aléatoires Waarschijnlijkheidstheorie Wahrscheinlichkeitsrechnung Zufallsvariable Probabilities Random variables Stochastic processes Statistische Nachrichtentheorie Wahrscheinlichkeitstheorie Wirtschaftlichkeitsrechnung Stochastisches Signal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001513684&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT papoulisathanasios probabilityrandomvariablesandstochasticprocesses |