Probability, random variables, and stochastic processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1984
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | McGraw-Hill series in electrical engineering / Communications and information theory
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 576 S. graph. Darst. |
| ISBN: | 0070484686 |
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| 245 | 1 | 0 | |a Probability, random variables, and stochastic processes |
| 250 | |a 2. ed. | ||
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Datensatz im Suchindex
| _version_ | 1804119275509645312 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Papoulis, Athanasios |
| author_facet | Papoulis, Athanasios |
| author_role | aut |
| author_sort | Papoulis, Athanasios |
| author_variant | a p ap |
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| bvnumber | BV005138700 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 SK 840 |
| ctrlnum | (OCoLC)9757552 (DE-599)BVBBV005138700 |
| 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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| indexdate | 2024-07-09T16:23:36Z |
| institution | BVB |
| isbn | 0070484686 |
| language | English |
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| physical | XV, 576 S. graph. Darst. |
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| publisher | McGraw-Hill |
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| spelling | Papoulis, Athanasios Verfasser aut Probability, random variables, and stochastic processes 2. ed. New York [u.a.] McGraw-Hill 1984 XV, 576 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in electrical engineering / Communications and information theory Probabilités Processus stochastiques Stochastische processen gtt Variables aléatoires Waarschijnlijkheidstheorie gtt Probabilities Random variables Stochastic processes Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Wirtschaftlichkeitsrechnung (DE-588)4066426-0 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Stochastisches Signal (DE-588)4140374-5 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Statistische Nachrichtentheorie (DE-588)4191729-7 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=003163828&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 Probability, random variables, and stochastic processes Probabilités Processus stochastiques Stochastische processen gtt Variables aléatoires Waarschijnlijkheidstheorie gtt Probabilities Random variables Stochastic processes Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Zufallsvariable (DE-588)4129514-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Wirtschaftlichkeitsrechnung (DE-588)4066426-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastisches Signal (DE-588)4140374-5 gnd Stochastik (DE-588)4121729-9 gnd Statistische Nachrichtentheorie (DE-588)4191729-7 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4129514-6 (DE-588)4057630-9 (DE-588)4066426-0 (DE-588)4079013-7 (DE-588)4140374-5 (DE-588)4121729-9 (DE-588)4191729-7 |
| 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 |
| title_fullStr | Probability, random variables, and stochastic processes |
| title_full_unstemmed | Probability, random variables, and stochastic processes |
| title_short | Probability, random variables, and stochastic processes |
| title_sort | probability random variables and stochastic processes |
| topic | Probabilités Processus stochastiques Stochastische processen gtt Variables aléatoires Waarschijnlijkheidstheorie gtt Probabilities Random variables Stochastic processes Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Zufallsvariable (DE-588)4129514-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Wirtschaftlichkeitsrechnung (DE-588)4066426-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastisches Signal (DE-588)4140374-5 gnd Stochastik (DE-588)4121729-9 gnd Statistische Nachrichtentheorie (DE-588)4191729-7 gnd |
| topic_facet | Probabilités Processus stochastiques Stochastische processen Variables aléatoires Waarschijnlijkheidstheorie Probabilities Random variables Stochastic processes Wahrscheinlichkeitsrechnung Zufallsvariable Stochastischer Prozess Wirtschaftlichkeitsrechnung Wahrscheinlichkeitstheorie Stochastisches Signal Stochastik Statistische Nachrichtentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003163828&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT papoulisathanasios probabilityrandomvariablesandstochasticprocesses |