Probability, random variables, and stochastic processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1991
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | McGraw-Hill series in electrical engineering : communications and signal processing
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XVII, 666 S. graph. Darst. |
| ISBN: | 0070484775 0070484686 |
Internformat
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| 100 | 1 | |a Papoulis, Athanasios |d 1921-2002 |e Verfasser |0 (DE-588)132599031 |4 aut | |
| 245 | 1 | 0 | |a Probability, random variables, and stochastic processes |c Athanasios Papoulis |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1991 | |
| 300 | |a XVII, 666 S. |b graph. Darst. | ||
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| 490 | 0 | |a McGraw-Hill series in electrical engineering : communications and signal processing | |
| 650 | 4 | |a Probabilités | |
| 650 | 4 | |a Procesos estocásticos | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 4 | |a Variables Random | |
| 650 | 4 | |a Variables aléatoires | |
| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a Random variables | |
| 650 | 4 | |a Stochastic processes | |
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Datensatz im Suchindex
| _version_ | 1804118682273579008 |
|---|---|
| adam_text | CONTENTS
Preface to the Third Edition xi
Preface to the Second Edition xiii
Preface to the First Edition xv
Part I 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
2 The Axioms of Probability 15
2 1 Set Theory 15
2 2 Probability Space 20
2 3 Conditional Probability 27
Problems 36
3 Repeated Trials 38
3 1 Combined Experiments 38
3 2 Bernoulli Trials 43
3 3 Asymptotic Theorems 47
3 4 Poisson Theorem and Random Points 55
Problems 60
4 The Concept of a Random Variable 63
4 1 Introduction 63
4 2 Distribution and Density Functions 66
vii
Viil CONTENTS
4 3 Special Cases 73
4 4 Conditional Distributions and Total Probability 79
Problems 84
5 Functions of One Random Variable 86
5 1 The Random Variable g(x) 86
5 2 The Distribution of g(x) 87
5 3 Mean and Variance 102
5 4 Moments 109
5 5 Characteristic Functions 115
Problems 120
6 Two Random Variables 124
6 1 Bivariate Distributions 124
6 2 One Function of Two Random Variables 135
6 3 Two Functions of Two Random Variables 142
Problems 148
7 Moments and Conditional Distributions 151
7 1 Joint Moments 151
7 2 Joint Characteristic Functions 157
7 3 Conditional Distributions 162
7 4 Conditional Expected Values 169
7 5 Mean Square Estimation 173
Problems 179
8 Sequences of Random Variables 182
8 1 General Concepts 182
8 2 Conditional Densities, Characteristic Functions,
and Normality 192
8 3 Mean Square Estimation 201
8 4 Stochastic Convergence and Limit Theorems 208
8 5 Random Numbers: Meaning and Generation 221
Problems 237
9 Statistics 241
9 1 Introduction 241
9 2 Parameter Estimation 244
9 3 Hypothesis Testing 265
Problems 279
Part II Stochastic Processes
10 General Concepts 285
10 1 Definitions 285
10 2 Systems with Stochastic Inputs 303
CONTENTS ix
10 3 The Power Spectrum 319
10 4 Digital Processes 332
Appendix 10A Continuity, Differentiation, Integration 336
Appendix 10B Shift Operators and Stationary Processes 339
Problems 340
11 Basic Applications 345
11 1 Random Walk, Brownian Motion, and Thermal Noise 345
11 2 Poisson Points and Shot Noise 354
11 3 Modulation 362
11 4 Cyclostationary Processes 373
11 5 Bandlimited Processes and Sampling Theory 376
11 6 Deterministic Signals in Noise 384
II 7 Bispectra and System Identification 389
Appendix 11A The Poisson Sum Formula 395
Appendix 11B Schwarz s Inequality 395
Problems 396
12 Spectral Representation 401
12 1 Factorization and Innovations 401
12 2 Finite Order Systems and State Variables 404
12 3 Fourier Series and Karhunen Loeve Expansions 412
12 4 Spectral Representation of Random Processes 416
Problems 425
13 Spectral Estimation 427
13 1 Ergodicity 427
13 2 Spectral Estimation 443
13 3 Extrapolation and System Identification 455
Appendix 13A Minimum Phase Functions 474
Appendix 13B All Pass Functions 475
Problems 477
14 Mean Square Estimation 480
14 1 Introduction 480
14 2 Prediction 487
14 3 Filtering and Prediction 508
14 4 Kalman Filters 515
Problems 529
15 Entropy 533
15 1 Introduction 533
15 2 Basic Concepts 542
15 3 Random Variables and Stochastic Processes 558
15 4 The Maximum Entropy Method 569
15 5 Coding 579
15 6 Channel Capacity 591
Problems 600
X CONTENTS
16 Selected Topics 603
16 1 The Level Crossing Problem 603
16 2 Queueing Theory 612
16 3 Shot Noise 629
16 4 Markoff Processes 635
Problems 654
Bibliography 658
Index 661
|
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| author | Papoulis, Athanasios 1921-2002 |
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| bvnumber | BV004550532 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 170 SK 800 SK 820 |
| classification_tum | MAT 600f ELT 502f |
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| 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 | Elektrotechnik Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:14:10Z |
| institution | BVB |
| isbn | 0070484775 0070484686 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002800050 |
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| physical | XVII, 666 S. graph. Darst. |
| publishDate | 1991 |
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| series2 | McGraw-Hill series in electrical engineering : communications and signal processing |
| spelling | Papoulis, Athanasios 1921-2002 Verfasser (DE-588)132599031 aut Probability, random variables, and stochastic processes Athanasios Papoulis 3. ed. New York [u.a.] McGraw-Hill 1991 XVII, 666 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in electrical engineering : communications and signal processing Probabilités Procesos estocásticos Processus stochastiques Variables Random Variables aléatoires Probabilities Random variables Stochastic processes Wirtschaftlichkeitsrechnung (DE-588)4066426-0 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Statistische Nachrichtentheorie (DE-588)4191729-7 gnd rswk-swf Stochastisches Signal (DE-588)4140374-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Stochastisches Signal (DE-588)4140374-5 s Statistische Nachrichtentheorie (DE-588)4191729-7 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Stochastischer Prozess (DE-588)4057630-9 s DE-188 Wirtschaftlichkeitsrechnung (DE-588)4066426-0 s Zufallsvariable (DE-588)4129514-6 s Stochastik (DE-588)4121729-9 s 1\p DE-604 http://www3.ub.tu-berlin.de/ihv/000137226.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002800050&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 |
| spellingShingle | Papoulis, Athanasios 1921-2002 Probability, random variables, and stochastic processes Probabilités Procesos estocásticos Processus stochastiques Variables Random Variables aléatoires Probabilities Random variables Stochastic processes Wirtschaftlichkeitsrechnung (DE-588)4066426-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistische Nachrichtentheorie (DE-588)4191729-7 gnd Stochastisches Signal (DE-588)4140374-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Zufallsvariable (DE-588)4129514-6 gnd Stochastik (DE-588)4121729-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4066426-0 (DE-588)4079013-7 (DE-588)4191729-7 (DE-588)4140374-5 (DE-588)4057630-9 (DE-588)4129514-6 (DE-588)4121729-9 (DE-588)4064324-4 |
| 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 | Probabilités Procesos estocásticos Processus stochastiques Variables Random Variables aléatoires Probabilities Random variables Stochastic processes Wirtschaftlichkeitsrechnung (DE-588)4066426-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistische Nachrichtentheorie (DE-588)4191729-7 gnd Stochastisches Signal (DE-588)4140374-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Zufallsvariable (DE-588)4129514-6 gnd Stochastik (DE-588)4121729-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Probabilités Procesos estocásticos Processus stochastiques Variables Random Variables aléatoires Probabilities Random variables Stochastic processes Wirtschaftlichkeitsrechnung Wahrscheinlichkeitstheorie Statistische Nachrichtentheorie Stochastisches Signal Stochastischer Prozess Zufallsvariable Stochastik Wahrscheinlichkeitsrechnung |
| url | http://www3.ub.tu-berlin.de/ihv/000137226.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002800050&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT papoulisathanasios probabilityrandomvariablesandstochasticprocesses |
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