The structure of probability theory with applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1969
|
| Schriftenreihe: | McGraw-Hill series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 746 S. |
Internformat
MARC
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| 100 | 1 | |a Thomasian, Aram J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The structure of probability theory with applications |c Aram J. Thomasian |
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1969 | |
| 300 | |a XVII, 746 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a McGraw-Hill series in probability and statistics | |
| 650 | 7 | |a Probabilidade (Textos Introdutorios) |2 larpcal | |
| 650 | 4 | |a Probabilities | |
| 650 | 0 | 7 | |a Wahrscheinlichkeit |0 (DE-588)4137007-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
PREFACE vii
CHAPTER I SETS I
l l Sets 1
1 2 Some set theory terminology 2
1 3 Operations on sets 4
1 4 Set identities 7
CHAPTER 2 COMBINATORICS 11
2 1 Cartesian products 11
2 2 The size of a cartesian product 13
2 3 Binomial coefficients 20
*2 4 The multinomial and hypergeometric formulas 30
CHAPTER 3 FUNCTIONS 36
3 1 Functions 36
3 2 Additional terminology concerning functions 40
3 3 Composition 41
3 4 Inverse images 43
3 5 One to one correspondence 46
CHAPTER 4 COUNTABILITY 49
4 1 Cardinality 49
4 2 Countable sets 50
4 3 An uncountable set 55
CHAPTER 5 ABSOLUTELY CONVERGENT SERIES 60
5 1 Review of series 60
5 2 Absolutely convergent series 62
5 3 Iterated summation 65
xiii
CHAPTER 6 DISCRETE PROBABILITY DENSITIES 68
6 1 The random wheel experiment 68
6 2 Discrete probability densities 70
6 3 Relative frequencies 75
6 4 Discrete probability measures 78
CHAPTER 7 INDEPENDENT EVENTS 88
7 1 Conditional probabilities 88
7 2 Bayes theorem 93
7 3 Independence of two events 96
7 4 Independence of n events 99
CHAPTER 8 INDEPENDENT EXPERIMENTS 103
8 1 Independent experiments 103
8 2 The binomial density 107
8 3 The Poisson density 113
8 4 The Pascal density 121
CHAPTER 9 THE MEAN AND VARIANCE 127
9 1 The mean of a density 127
9 2 The variance of a density 131
9 3 A linear transformation of a density 135
9 4 The moment generating function 138
CHAPTER 10 THE LAW OF LARGE NUMBERS FOR BERNOULLI TRIALS 146
10 1 Chebychev s inequality 146
10 2 The law of large numbers for Bernoulli trials 153
*IO 3 The Weierstrass approximation theorem 155
CHAPTER | | RANDOM VARIABLES 161
ll l Random points and random variables 161
M 2 Independent random variables 174
11 3 Expectation 183
IM Correlation and linear prediction 202
xiv
CHAPTER 12 THE LAW OF LARGE NUMBERS 212
12 1 The weak law of large numbers 213
12 2 Sampling experiments 219
12 3 The strong law of large numbers 225
*l2 4 The proof of the strong law of large numbers 228
CHAPTER 13 THE CENTRAL LIMIT THEOREM 233
13 1 The normal density 233
13 2 The central limit theorem 239
*l3 3 The normal approximation to the binomial 251
*l3 4 A numerical example 256
CHAPTER 14 CONDITIONAL EXPECTATIONS
AND BRANCHING PROCESSES 261
*I4 I Conditional expectation 261
?14 2 The sum of a random number of random variables 274
?14 3 Branching processes 286
CHAPTER 15 PROBABILITY SPACES 295
15 1 Probability spaces 295
15 2 Induced distributions 298
15 3 Independence 302
15 4 Expectation 306
*l5 5 Conditional expectation 314
CHAPTER 16 CONTINUOUS PROBABILITY DENSITIES 320
16 1 Continuous probability densities 320
16 2 The density of Y = g(X) 339
16 3 Induced densities, n 2 354
16 4 Independence 366
16 5 Expectation 379
?16 6 Conditional expectations 395
CHAPTER 17 DISTRIBUTION FUNCTIONS 404
17 1 Distribution functions on R 404
17 2 The distribution function of Y = g(X) 422
17 3 Distribution functions on Rn 434
?17 4 The method of indicators 440
XV
CHAPTER 18 MULTIVARIATE NORMAL DENSITIES
AND CHARACTERISTIC FUNCTIONS 447
18 1 Covariance matrices and linear prediction 447
18 2 Multivariate normal densities 457
18 3 Characteristic functions 467
18 4 A vector central limit theorem 479
CHAPTER 19 PROOF OF THE CENTRAL LIMIT THEOREM 483
CHAPTER 20 THE METHOD OF TRUNCATION 494
20 1 The method of truncation and the WLLN 494
20 2 The central limit theorem and truncation 500
20 3 The strong law of large numbers and truncation 505
CHAPTER 21 PROBABILITY SPACES: A RIGOROUS PRESENTATION 513
21 1 Probability spaces 514
21 2 Borel sets 515
21 3 Random variables and independence 519
21 4 Expectation 524
CHAPTER 22 INTRODUCTION TO STOCHASTIC PROCESSES 527
22 1 Introduction 528
22 2 Consistent families, and processes having
stationary independent increments 537
22 3 Construction and uniqueness of processes 546
CHAPTER 23 THE POISSON PROCESS AND SOME OF ITS
GENERALIZATIONS 556
23 1 Introduction 557
23 2 The uniqueness of the Poisson process 565
23 3 Two characterizations of a Poisson process 570
23 4 Compound Poisson processes 581
23 5 Nonhomogeneous Poisson processes 584
23 6 Pure birth processes 588
23 7 Birth and death processes 596
CHAPTER 24 THE WIENER PROCESS 603
24 1 Introduction 603
24 2 Some simple properties of Wiener processes 609
24 3 Covariance functions and normal processes 623
xvi
APPENDIX I SEVERAL FREQUENTLY USED FORMULAS 629
APPENDIX 2 THE SUPREMUM 630
APPENDIX 3 SUMMABILITY 634
SUMMARIES 639
SELECTED ANSWERS AND SOLUTIONS 727
INDEX 741
xvii
|
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| indexdate | 2024-07-09T15:51:36Z |
| institution | BVB |
| language | English |
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| physical | XVII, 746 S. |
| psigel | TUB-nveb HUB-ZB011201202 |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | McGraw-Hill series in probability and statistics |
| spelling | Thomasian, Aram J. Verfasser aut The structure of probability theory with applications Aram J. Thomasian New York [u.a.] McGraw-Hill 1969 XVII, 746 S. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in probability and statistics Probabilidade (Textos Introdutorios) larpcal Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Struktur (DE-588)4058125-1 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 s Theorie (DE-588)4059787-8 s Struktur (DE-588)4058125-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001859872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thomasian, Aram J. The structure of probability theory with applications Probabilidade (Textos Introdutorios) larpcal Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd Struktur (DE-588)4058125-1 gnd Theorie (DE-588)4059787-8 gnd |
| subject_GND | (DE-588)4137007-7 (DE-588)4058125-1 (DE-588)4059787-8 |
| title | The structure of probability theory with applications |
| title_auth | The structure of probability theory with applications |
| title_exact_search | The structure of probability theory with applications |
| title_full | The structure of probability theory with applications Aram J. Thomasian |
| title_fullStr | The structure of probability theory with applications Aram J. Thomasian |
| title_full_unstemmed | The structure of probability theory with applications Aram J. Thomasian |
| title_short | The structure of probability theory with applications |
| title_sort | the structure of probability theory with applications |
| topic | Probabilidade (Textos Introdutorios) larpcal Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd Struktur (DE-588)4058125-1 gnd Theorie (DE-588)4059787-8 gnd |
| topic_facet | Probabilidade (Textos Introdutorios) Probabilities Wahrscheinlichkeit Struktur Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001859872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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