Fundamentals of probability:
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
2024
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| Edition: | Fifth edition, international student edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxv, 672 Seiten Illustrationen, Diagramme |
| ISBN: | 9781032803531 9781032366081 |
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Contents ► Preface ► 1 xvii Axioms of Probability 1 1.1 1.2 Introduction 1 Sample Space and Events 4 Fields and σ-Fields 9 1.3 Axioms of Probability 17 1.4 Basic Theorems 23 1.5 Continuity of Probability Function 34 1.6 Probabilities 0 and 1 36 1.7 Random Selection of Points from Intervals 1.8 Randomness and Uncertainty 42 1.9 What Is Simulation? 43 1.10 A Concise Study of R 45 Chapter 1 Summary 60 Review Problems 62 Self-Test on Chapter 1 65 Combinatorial Methods к 2 2.1 2.2 Introduction 69 Counting Principle 69 Number of Subsets of a Set Tree Diagrams 75 Permutations 80 Combinations 88 Binomial Expansion 95 Pascal’s Triangle 99 Stirling’s Formula 109 Combinatorial Simulation in R Chapter 2 Summary 113 Review Problems 114 Self-Test on Chapter 2 118 2.3 2.4 2.5 2.6 37 69 74 110 vii
viii Contents Conditional Probability and Independence ► 3 3.1 Conditional Probability 121 Reduction of Sample Space 126 The Multiplication Rule 132 Law of Total Probability 136 Bayes’ Formula 147 Independence 157 R Simulation for Conditional Probabilities Chapter 3 Summary 179 Review Problems 181 Self-Test on Chapter 3 184 3.2 3.3 3.4 3.5 3.6 175 Distribution Functions and Discrete Random Variables ► 4 4.1 4.2 4.3 4.4 4.5 Random Variables 187 Distribution Functions 191 Discrete Random Variables 201 Expectations of Discrete Random Variables 209 Variances and Moments of Discrete Random Variables Moments 227 Standardized Random Variables 230 Joint Probability Mass Functions 232 Independence of Discrete Random Variables 247 Simulating Discrete Random Variables in R 253 Chapter 4 Summary 257 Review Problems 261 Self-Test on Chapter 4 264 4.6 4.7 4.8 4.9 222 Continuous Random Variables ► 5 5.1 5.2 5.3 Probability Density Functions 267 Density Function of a Function of a Random Variable 278 Expectations and Variances of Continuous Random Variables Expectations of Continuous Random Variables 284 Variances of Continuous Random Variables 290 Joint Probability Density Functions 298 Independence of Continuous Random Variables 320 Random Sample 325 Chapter 5 Summary 330 Review Problems 334 Self-Test on Chapter 5 338 5.4 5.5 121 267 284
Contents 6 6.1 Bernoulli and Binomial Random Variables 341 Expectations and Variances of Binomial Random Variables Poisson Random Variable 357 Poisson as an Approximation to Binomial 357 Poisson Process 362 Other Discrete Random Variables 373 Geometric Random Variable 373 Negative Binomial Random Variable 376 Hypergeometric Random Variable 379 Binomial and Hypergeometric Relationships 385 Multinomial Distributions 392 Simulating Special Discrete Distributions Using R 396 Chapter 6 Summary 401 Review Problems 404 Self-Test on Chapter 6 408 6.2 6.3 6.4 6.5 Special Continuous Distributions ► 7 7.1 7.2 Uniform Random Variable 411 Normal Random Variables 418 Standard Normal Random Variables 418 Correction for Continuity 421 Normal Random Variables with Varying Parameters 424 Central Limit Theorem 432 Exponential Random Variables 440 Gamma Distribution 449 Beta Distribution 456 Survival Analysis and Hazard Function 462 Simulating Special Continuous Distributions Using R 467 Chapter 7 Summary 474 Review Problems 477 Self-Test on Chapter 7 479 7.3 7.4 7.5 7.6 Ί.Ί 7.8 341 Special Discrete Distributions ► ix 347 411
X Contents Understanding Relationships: Covariance, Correlations, and Conditional Distributions 8.1 8.2 8.3 8.4 8.5 Introduction 481 Covariance 481 Correlation 494 Conditional Distributions 501 Conditional Distributions: Discrete Case 501 Conditional Distributions: Continuous Case 507 Conditional Distributions in Higher Dimensions 511 Transformations of Two Random Variables 520 Convolution Theorem 523 Chapter 8 Summary 529 Review Problems 532 Self-Test on Chapter 8 534 More Bivariate and Multivariate Topics ► 9 9.1 9.2 9.3 Conditioning on Random Variables 537 Order Statistics 552 Order Statistics Simulation with R 557 Bivariate Normal Distribution 559 Chapter 9 Summary 565 Review Problems 567 Self-Test on Chapter 9 569 ► 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 Inequalities and Limit Theorems Moment-Generating Functions 571 Further Applications of Moment-Generating Functions 585 Characteristic Functions 594 Inversion Theorem 601 Lévy Continuity Theorem for Characteristic Functions 606 Markov and Chebyshev Inequalities 610 Chebyshev ’s Inequality and Sample Mean 614 Laws of Large Numbers 620 Two Proofs for Central Limit Theorem 629 More on R Simulations 632 Monte Carlo Method 634 Chapter 10 Summary 637 Review Problems 641 Self-Test on Chapter 10 643 537 571
Contents xi ► Appendix Tables 647 к* Answers to Odd-Numbered Exercises 653 ► Index 665 |
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| author | Ghahramani, Saeed ca. 20./21. Jh |
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| edition | Fifth edition, international student edition |
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| illustrated | Illustrated |
| indexdate | 2025-02-17T15:02:47Z |
| institution | BVB |
| isbn | 9781032803531 9781032366081 |
| language | English |
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| physical | xxv, 672 Seiten Illustrationen, Diagramme |
| publishDate | 2024 |
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| publisher | CRC Press, Taylor & Francis Group |
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| spelling | Ghahramani, Saeed ca. 20./21. Jh. Verfasser (DE-588)1356086837 aut Fundamentals of probability Saeed Gharamani Fifth edition, international student edition Boca Raton ; London ; New York CRC Press, Taylor & Francis Group 2024 xxv, 672 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-0033-3289-3 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035207096&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ghahramani, Saeed ca. 20./21. Jh Fundamentals of probability Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4079013-7 |
| title | Fundamentals of probability |
| title_auth | Fundamentals of probability |
| title_exact_search | Fundamentals of probability |
| title_full | Fundamentals of probability Saeed Gharamani |
| title_fullStr | Fundamentals of probability Saeed Gharamani |
| title_full_unstemmed | Fundamentals of probability Saeed Gharamani |
| title_short | Fundamentals of probability |
| title_sort | fundamentals of probability |
| topic | Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Wahrscheinlichkeitstheorie |
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