Probability theory: an introduction using R
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
2025
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| Edition: | First edition |
| Series: | A Chapman & Hall book
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xx, 575 Seiten Diagramme |
| ISBN: | 9781032617978 9781032619033 |
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Contents List of Tables List of Figures Author Biographies Sigma Field, Borel Field andProbability Measure 1.1 1.2 1.3 1.4 1.5 l.G 1.7 1.8 2 xiii xv Preface 1 xi xix 1 Introduction. I Introduction to R Software and Language . 2 Limit of a Sequence of Sets . 3 Borel Field . 31 Probability SpaceH Conceptual Exercises. 5s Computational Exercises. 62 Multiple Choice Questions. 62 Random Variables and Random Vectors 67 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 17 6s si U h 121 127 123 130 Introduction. Random Variables . Random Vectors . Simple Random Variable. Probability Distribution of a Random Variable . Conceptual Exercises. Computational Exercises. Multiple Choice Questions. 3
Distribution Function 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Introduction. Properties of a Distribution Function. Decomposition of a Distribution Function . Distribution Function of a Random Vector. Conceptual Exercises. Computational Exercises. Multiple Choice Questions. 135 135 136 115 15s 16 I 162 IG2
νϋί Contents Expectation andCharacteristic Function 4.1 Introduction. 4.2 Expectation of a Simple Random Variable. 4.3 Expectation of Non-Negative and Arbitrary Random Variables . 4.4 Characteristic Function . 4.5 Moment Inequalities . 4.6 Conceptual Exercises. 4.7 Multiple Choice Questions . 165 16o 167 5 Independence 5.1 Introduction. 5.2 Independence of Events and Classes ofEvents. 5.3 Independence of Random Variables. 5.4 Kolmogorov Zero-One Law . 5.5 Conceptual Exercises. 5.6 Multiple Choice Questions. 221 221 222 227 242 246 248 6 Almost Sure Convergence and BorelZero-One Law 6.1 Introduction. 6.2 Definitions of Various Modes of Convergence . 6.3 Almost Sure Convergence .
6.4 Dorel Zero-One Law . 6.5 Conceptual Exercises. 6.6 Computational Exercises. 6.7 Multiple Choice Questions. 252 252 253 257 27Ü 284 286 286 7 Convergence in Probability, in Law and in r-th Mean 7.1 Introduction. 7.2 Convergence in Probability . 7.3 Convergence in Law . 7.4 Convergence in r-th Mean. 7.5 Conceptual Exercises. 7.6 Computational Exercises. 7.7 Multiple Choice Questions. 288 288 288 316 353 371 375 376 4 171 185 203 214 217 8 Convergence of a Sequence of Expectations 386 8.1 Introduction. 386 8.2 Monotone Convergence Theorem . 387 8.3 Lebesgue Dominated Probability Convergence Theorem 398 8.4 Conceptual Exercises. 403 8.5 Computational
Exercises. 403 8.6 Multiple Choice Questions. 403
ix Contents of Largo Numbers Introduction. Weak Law of Large Numbers . Strong Law of Large Numbers. Conceptual Exercises. Computational Exercises. Multiple Choice Questions. 4Ш» И”» 4(,7 И9 42· 127 127 10 Central Limit Theorem 10.1 Introduction. 10.2 Lindeberg-Levy CLT. 10.3 CLT for Independent Random Variables . 10.4 Conceptual Exercises. 10.5 Computational Exercises. 10.6 Multiple Choice Questions. 130 130 131 45] 1'3 171 175 11 Solutions to Conceptual Exercises 11.1 Chapter 1 . 11.2 Chapter 2 . 11.3 Chapter 3. 11,4 Chapter 4. 11.5 Chapter
5. 11.6 Chapter 6. 11,7 Chapter 7. 11.8 Chapters. 11.9 Chapter 9 . 11.10 Chapter 10 . 479 479 196 503 59 s 519 526 632 553 556 56] Bibliography 571 Index 573 9 Laws 9.1 9.2 9.3 9.4 9.5 9.G |
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| dewey-sort | 3519.20285 45133 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | First edition |
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| spelling | Deshmukh, Shailaja Verfasser (DE-588)1089598947 aut Probability theory an introduction using R Shailaja R. Deshmukh and Akanksha S. Kashikar First edition Boca Raton ; London ; New York CRC Press, Taylor & Francis Group 2025 xx, 575 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Includes bibliographical references and index R Programm (DE-588)4705956-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Probabilities / Data processing / Textbooks R (Computer program language) / Textbooks (DE-588)4123623-3 Lehrbuch gnd-content Wahrscheinlichkeitstheorie (DE-588)4079013-7 s R Programm (DE-588)4705956-4 s b DE-604 Kashikar, Akanksha S. Verfasser aut Erscheint auch als Online-Ausgabe 978-1-03-261905-7 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035260684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Deshmukh, Shailaja Kashikar, Akanksha S. Probability theory an introduction using R R Programm (DE-588)4705956-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4079013-7 (DE-588)4123623-3 |
| title | Probability theory an introduction using R |
| title_auth | Probability theory an introduction using R |
| title_exact_search | Probability theory an introduction using R |
| title_full | Probability theory an introduction using R Shailaja R. Deshmukh and Akanksha S. Kashikar |
| title_fullStr | Probability theory an introduction using R Shailaja R. Deshmukh and Akanksha S. Kashikar |
| title_full_unstemmed | Probability theory an introduction using R Shailaja R. Deshmukh and Akanksha S. Kashikar |
| title_short | Probability theory |
| title_sort | probability theory an introduction using r |
| title_sub | an introduction using R |
| topic | R Programm (DE-588)4705956-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | R Programm Wahrscheinlichkeitstheorie Lehrbuch |
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