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 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV002970575 | ||
| 003 | DE-604 | ||
| 005 | 20120324 | ||
| 007 | t | ||
| 008 | 900725s1969 |||| 00||| eng d | ||
| 035 | |a (OCoLC)11792 | ||
| 035 | |a (DE-599)BVBBV002970575 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-19 |a DE-29T |a DE-83 |a DE-188 |a DE-11 | ||
| 050 | 0 | |a QA273 | |
| 082 | 0 | |a 519/.1 |2 18 | |
| 084 | |a QH 170 |0 (DE-625)141536: |2 rvk | ||
| 084 | |a SK 800 |0 (DE-625)143256: |2 rvk | ||
| 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 |
| 650 | 0 | 7 | |a Struktur |0 (DE-588)4058125-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Theorie |0 (DE-588)4059787-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Wahrscheinlichkeit |0 (DE-588)4137007-7 |D s |
| 689 | 0 | 1 | |a Theorie |0 (DE-588)4059787-8 |D s |
| 689 | 0 | 2 | |a Struktur |0 (DE-588)4058125-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 940 | 1 | |q TUB-nveb | |
| 940 | 1 | |q HUB-ZB011201202 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001859872 | ||
Datensatz im Suchindex
| _version_ | 1804117261677494272 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Thomasian, Aram J. |
| author_facet | Thomasian, Aram J. |
| author_role | aut |
| author_sort | Thomasian, Aram J. |
| author_variant | a j t aj ajt |
| building | Verbundindex |
| bvnumber | BV002970575 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273 |
| callnumber-search | QA273 |
| callnumber-sort | QA 3273 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 170 SK 800 |
| ctrlnum | (OCoLC)11792 (DE-599)BVBBV002970575 |
| dewey-full | 519/.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519/.1 |
| dewey-search | 519/.1 |
| dewey-sort | 3519 11 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01674nam a2200445 c 4500</leader><controlfield tag="001">BV002970575</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20120324 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">900725s1969 |||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)11792</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002970575</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA273</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519/.1</subfield><subfield code="2">18</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 170</subfield><subfield code="0">(DE-625)141536:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 800</subfield><subfield code="0">(DE-625)143256:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Thomasian, Aram J.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The structure of probability theory with applications</subfield><subfield code="c">Aram J. Thomasian</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">McGraw-Hill</subfield><subfield code="c">1969</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVII, 746 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">McGraw-Hill series in probability and statistics</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Probabilidade (Textos Introdutorios)</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probabilities</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Wahrscheinlichkeit</subfield><subfield code="0">(DE-588)4137007-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Struktur</subfield><subfield code="0">(DE-588)4058125-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Theorie</subfield><subfield code="0">(DE-588)4059787-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Wahrscheinlichkeit</subfield><subfield code="0">(DE-588)4137007-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Theorie</subfield><subfield code="0">(DE-588)4059787-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Struktur</subfield><subfield code="0">(DE-588)4058125-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">TUB-nveb</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">HUB-ZB011201202</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001859872</subfield></datafield></record></collection> |
| id | DE-604.BV002970575 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:51:36Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001859872 |
| oclc_num | 11792 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-29T DE-83 DE-188 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-29T DE-83 DE-188 DE-11 |
| 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 |
| work_keys_str_mv | AT thomasianaramj thestructureofprobabilitytheorywithapplications |