A natural introduction to probability theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2008
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 197 S. graph. Darst. |
| ISBN: | 9783764387235 |
Staff View
MARC
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| 100 | 1 | |a Meester, Ronald |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A natural introduction to probability theory |c Ronald Meester |
| 246 | 1 | 3 | |a Introduction to probability theory |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a X, 197 S. |b graph. Darst. | ||
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| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a Stochastic processes | |
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Record in the Search Index
| _version_ | 1804137919653347328 |
|---|---|
| adam_text | RONALD MEESTER A NATURAL INTRODUCTION TO PROBABILITY THEORY SECOND
EDITION BIRKHDUSER BASEL * BOSTON * BERLIN CONTENTS PREFACE TO THE FIRST
EDITION VIII PREFACE TO THE SECOND EDITION X 1 EXPERIMENTS 1 1.1
DEFINITIONS AND EXAMPLES 1 1.2 COUNTING AND COMBINATORICS 6 1.3
PROPERTIES OF PROBABILITY MEASURES 10 1.4 CONDITIONAL PROBABILITIES 12
1.5 INDEPENDENCE 18 1.6 A FIRST LAW OF LARGE NUMBERS 26 1.7 EXERCISES 28
2 RANDOM VARIABLES AND RANDOM VECTORS 35 2.1 RANDOM VARIABLES 35 2.2
INDEPENDENCE 41 2.3 EXPECTATION AND VARIANCE 43 2.4 RANDOM VECTORS 52
2.5 CONDITIONAL DISTRIBUTIONS AND EXPECTATIONS 57 2.6 GENERATING
FUNCTIONS 62 2.7 EXERCISES 64 3 RANDOM WALK 71 3.1 RANDOM WALK AND
COUNTING 71 3.2 THE ARC-SINE LAW 75 3.3 EXERCISES 78 4 LIMIT THEOREMS 81
4.1 THE LAW OF LARGE NUMBERS 81 4.2 THE CENTRAL LIMIT, THEOREM 85 4.3
EXERCISES 88 V J CONTENTS I INTERMEZZO 89 1.1 UNCOUNTABLE SAMPLE SPACES
89 1.2 AN EVENT WITHOUT A PROBABILITY?! 90 1.3 RANDOM VARIABLES ON
UNCOUNTABLE SAMPLE SPACES 92 5 CONTINUOUS RANDOM VARIABLES AND VECTORS
93 5.1 EXPERIMENTS 93 5.2 PROPERTIES OF PROBABILITY MEASURES 98 5.3
CONTINUOUS RANDOM VARIABLES 100 5.4 EXPECTATION 105 5.5 RANDOM VECTORS
AND INDEPENDENCE 109 5.6 FUNCTIONS OF RANDOM VARIABLES AND VECTORS 113
5.7 SUMS OF RANDOM VARIABLES 117 5.8 MORE ABOUT THE EXPECTATION;
VARIANCE 118 5.9 RANDOM VARIABLES WHICH ARE NEITHER DISCRETE NOR
CONTINUOUS . . 122 5.10 CONDITIONAL DISTRIBUTIONS AND EXPECTATIONS 124
5.11 THE LAW OF LARGE NUMBERS 131 5.12 EXERCISES 131 6 INFINITELY MANY
REPETITIONS 137 6.1 INFINITELY MANY COIN FLIPS AND RANDOM POINTS IN
(0,1] 138 6.2 A MORE GENERAL APPROACH TO INFINITELY MANY REPETITIONS 140
6.3 THE STRONG LAW OF LARGE NUMBERS 142 6.4 RANDOM WALK REVISITED 146
6.5 BRANCHING PROCESSES 147 6.6 EXERCISES 151 7 THE POISSON PROCESS 153
7.1 BUILDING A MODEL 153 7.2 BASIC PROPERTIES 158 7.3 THE WAITING TIME
PARADOX 162 7.4 THE STRONG LAW OF LARGE NUMBERS 164 7.5 EXERCISES 165 8
LIMIT THEOREMS 167 8.1 WEAK CONVERGENCE 167 8.2 CHARACTERISTIC FUNCTIONS
169 8.3 EXPANSION OF THE CHARACTERISTIC FUNCTION 173 8.4 THE LAW OF
LARGE NUMBERS 176 8.5 THE CENTRAL LIMIT THEOREM 179 8.6 EXERCISES 180 9
EXTENDING THE PROBABILITIES 183 9.1 GENERAL PROBABILITY MEASURES 183
CONTENTS VII A INTERPRETING PROBABILITIES 187 B FURTHER READING 191 C
ANSWERS TO SELECTED EXERCISES 193 INDEX 195
|
| adam_txt |
RONALD MEESTER A NATURAL INTRODUCTION TO PROBABILITY THEORY SECOND
EDITION BIRKHDUSER BASEL * BOSTON * BERLIN CONTENTS PREFACE TO THE FIRST
EDITION VIII PREFACE TO THE SECOND EDITION X 1 EXPERIMENTS 1 1.1
DEFINITIONS AND EXAMPLES 1 1.2 COUNTING AND COMBINATORICS 6 1.3
PROPERTIES OF PROBABILITY MEASURES 10 1.4 CONDITIONAL PROBABILITIES 12
1.5 INDEPENDENCE 18 1.6 A FIRST LAW OF LARGE NUMBERS 26 1.7 EXERCISES 28
2 RANDOM VARIABLES AND RANDOM VECTORS 35 2.1 RANDOM VARIABLES 35 2.2
INDEPENDENCE 41 2.3 EXPECTATION AND VARIANCE 43 2.4 RANDOM VECTORS 52
2.5 CONDITIONAL DISTRIBUTIONS AND EXPECTATIONS 57 2.6 GENERATING
FUNCTIONS 62 2.7 EXERCISES 64 3 RANDOM WALK 71 3.1 RANDOM WALK AND
COUNTING 71 3.2 THE ARC-SINE LAW 75 3.3 EXERCISES 78 4 LIMIT THEOREMS 81
4.1 THE LAW OF LARGE NUMBERS 81 4.2 THE CENTRAL LIMIT, THEOREM 85 4.3
EXERCISES 88 V J CONTENTS I INTERMEZZO 89 1.1 UNCOUNTABLE SAMPLE SPACES
89 1.2 AN EVENT WITHOUT A PROBABILITY?! 90 1.3 RANDOM VARIABLES ON
UNCOUNTABLE SAMPLE SPACES 92 5 CONTINUOUS RANDOM VARIABLES AND VECTORS
93 5.1 EXPERIMENTS 93 5.2 PROPERTIES OF PROBABILITY MEASURES 98 5.3
CONTINUOUS RANDOM VARIABLES 100 5.4 EXPECTATION 105 5.5 RANDOM VECTORS
AND INDEPENDENCE 109 5.6 FUNCTIONS OF RANDOM VARIABLES AND VECTORS 113
5.7 SUMS OF RANDOM VARIABLES 117 5.8 MORE ABOUT THE EXPECTATION;
VARIANCE 118 5.9 RANDOM VARIABLES WHICH ARE NEITHER DISCRETE NOR
CONTINUOUS . . 122 5.10 CONDITIONAL DISTRIBUTIONS AND EXPECTATIONS 124
5.11 THE LAW OF LARGE NUMBERS 131 5.12 EXERCISES 131 6 INFINITELY MANY
REPETITIONS 137 6.1 INFINITELY MANY COIN FLIPS AND RANDOM POINTS IN
(0,1] 138 6.2 A MORE GENERAL APPROACH TO INFINITELY MANY REPETITIONS 140
6.3 THE STRONG LAW OF LARGE NUMBERS 142 6.4 RANDOM WALK REVISITED 146
6.5 BRANCHING PROCESSES 147 6.6 EXERCISES 151 7 THE POISSON PROCESS 153
7.1 BUILDING A MODEL 153 7.2 BASIC PROPERTIES 158 7.3 THE WAITING TIME
PARADOX 162 7.4 THE STRONG LAW OF LARGE NUMBERS 164 7.5 EXERCISES 165 8
LIMIT THEOREMS 167 8.1 WEAK CONVERGENCE 167 8.2 CHARACTERISTIC FUNCTIONS
169 8.3 EXPANSION OF THE CHARACTERISTIC FUNCTION 173 8.4 THE LAW OF
LARGE NUMBERS 176 8.5 THE CENTRAL LIMIT THEOREM 179 8.6 EXERCISES 180 9
EXTENDING THE PROBABILITIES 183 9.1 GENERAL PROBABILITY MEASURES 183
CONTENTS VII A INTERPRETING PROBABILITIES 187 B FURTHER READING 191 C
ANSWERS TO SELECTED EXERCISES 193 INDEX 195 |
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| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
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| illustrated | Illustrated |
| index_date | 2024-07-02T21:41:03Z |
| indexdate | 2024-07-09T21:19:57Z |
| institution | BVB |
| isbn | 9783764387235 |
| language | English |
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| physical | X, 197 S. graph. Darst. |
| publishDate | 2008 |
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| publisher | Birkhäuser |
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| spelling | Meester, Ronald Verfasser aut A natural introduction to probability theory Ronald Meester Introduction to probability theory 2. ed. Basel [u.a.] Birkhäuser 2008 X, 197 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probabilities Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Erscheint auch als Online-Ausgabe 978-3-7643-8724-2 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016672155&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meester, Ronald A natural introduction to probability theory Probabilities Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4079013-7 |
| title | A natural introduction to probability theory |
| title_alt | Introduction to probability theory |
| title_auth | A natural introduction to probability theory |
| title_exact_search | A natural introduction to probability theory |
| title_exact_search_txtP | A natural introduction to probability theory |
| title_full | A natural introduction to probability theory Ronald Meester |
| title_fullStr | A natural introduction to probability theory Ronald Meester |
| title_full_unstemmed | A natural introduction to probability theory Ronald Meester |
| title_short | A natural introduction to probability theory |
| title_sort | a natural introduction to probability theory |
| topic | Probabilities Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Probabilities Stochastic processes Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016672155&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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