Probability and statistics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. u.a.
Addison-Wesley
2002
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Addison-Wesley series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 816 S. Ill. |
| ISBN: | 0321204735 0201524880 |
Internformat
MARC
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| 250 | |a 3. ed. | ||
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Datensatz im Suchindex
| _version_ | 1804136220928770048 |
|---|---|
| adam_text | Contents
Preface xi
1 Introduction to Probability 1
1.1 The History of Probability 1
1.2 Interpretations of Probability 2
1.3 Experiments and Events 5
1.4 Set Theory 6
1.5 The Definition of Probability 12
1.6 Finite Sample Spaces 19
1.7 Counting Methods 22
1.8 Combinatorial Methods 28
1.9 Multinomial Coefficients 35
1.10 The Probability of a Union of Events 39
1.11 Statistical Swindles 45
1.12 Supplementary Exercises 47
^ Conditional Probability 49
2.1 The Definition of Conditional Probability 49
2.2 Independent Events 56
2.3 Bayes Theorem 66
* 2.4 Markov Chains 79
* 2.5 The Gambler s Ruin Problem 89
2.6 Supplementary Exercises 93
Contents
3 Random Variables and Distributions 97
3.1 Random Variables and Discrete Distributions 97
3.2 Continuous Distributions 103
3.3 The Distribution Function 109
3.4 Bivariate Distributions 118
3.5 Marginal Distributions 128
3.6 Conditional Distributions 136
3.7 Multivariate Distributions 146
3.8 Functions of a Random Variable 158
3.9 Functions of Two or More Random Variables 165
3.10 Supplementary Exercises 176
4 Expectation isi
4.1 The Expectation of a Random Variable 181
4.2 Properties of Expectations 189
4.3 Variance 197
4.4 Moments 203
4.5 The Mean and the Median 209
4.6 Covariance and Correlation 214
4.7 Conditional Expectation 222
4.8 The Sample Mean 229
* 4.9 Utility 236
4.10 Supplementary Exercises 243
5 Special Distributions 247
5.1 Introduction 247
5.2 The Bernoulli and Binomial Distributions 247
5.3 The Hypergeometric Distribution 251
5.4 The Poisson Distribution 255
5.5 The Negative Binomial Distribution 263
5.6 The Normal Distribution 268
5.7 The Central Limit Theorem 282
5.8 The Correction for Continuity 291
5.9 The Gamma Distribution 295
5.10 The Beta Distribution 303
5.11 The Multinomial Distribution 309
5.12 The Bivariate Normal Distribution 313
5.13 Supplementary Exercises 320
Contents
O Estimation 323
6.1 Statistical Inference 323
6.2 Prior and Posterior Distributions 327
6.3 Conjugate Prior Distributions 335
6.4 Bayes Estimators 346
6.5 Maximum Likelihood Estimators 355
6.6 Properties of Maximum Likelihood Estimators 364
* 6.7 Sufficient Statistics 370
* 6.8 Jointly Sufficient Statistics 377
* 6.9 Improving an Estimator 383
6.10 Supplementary Exercises 389
/ Sampling Distributions of Estimators 391
7.1 The Sampling Distribution of a Statistic 391
7.2 The Chi Square Distribution 393
7.3 Joint Distribution of the Sample Mean and Sample Variance 39
7.4 The t Distribution 404
7.5 Confidence Intervals 409
*7.6 Bayesian Analysis of Samples from a Normal Distribution 416
7.7 Unbiased Estimators 427
* 7.8 Fisher Information 435
7.9 Supplementary Exercises 446
O Testing Hypotheses 449
8.1 Problems of Testing Hypotheses 449
* 8.2 Testing Simple Hypotheses 463
* 8.3 Uniformly Most Powerful Tests 470
* 8.4 Two Sided Alternatives 479
8.5 The t Test 485
8.6 Comparing the Means of Two Normal Distributions 498
8.7 The F Distribution 506
*8.8 Bayes Test Procedures 514
* 8.9 Foundational Issues 527
8.10 Supplementary Exercises 531
9 Categorical Data and Nonparametric Methods
9.1 Tests of Goodness of Fit 535
Contents
9.2 Goodness of Fit for Composite Hypotheses 542
9.3 Contingency Tables 550
9.4 Tests of Homogeneity 556
9.5 Simpson s Paradox 562
* 9.6 Kolmogorov Smirnov Tests 566
* 9.7 Robust Estimation 575
* 9.8 Sign and Rank Tests 587
9.9 Supplementary Exercises 595
10 Linear Statistical Models 599
10.1 The Method of Least Squares 599
10.2 Regression 609
10.3 Statistical Inference in Simple Linear Regression 618
* 10.4 Bayesian Inference in Simple Linear Regression 638
10.5 The General Linear Model and Multiple Regression 645
10.6 Analysis of Variance 665
* 10.7 The Two Way Layout 673
* 10.8 The Two Way Layout with Replications 683
10.9 Supplementary Exercises 694
X 1 Simulation 699
11.1 Why Is Simulation Useful? 699
11.2 Simulating Specific Distributions 713
11.3 Importance Sampling 727
* 11.4 Markov Chain Monte Carlo 735
11.5 The Bootstrap 753
11.6 Supplementary Exercises 765
Tables 769
Answers to Odd Numbered Exercises 781
References 801
Index 807
|
| adam_txt |
Contents
Preface xi
1 Introduction to Probability 1
1.1 The History of Probability 1
1.2 Interpretations of Probability 2
1.3 Experiments and Events 5
1.4 Set Theory 6
1.5 The Definition of Probability 12
1.6 Finite Sample Spaces 19
1.7 Counting Methods 22
1.8 Combinatorial Methods 28
1.9 Multinomial Coefficients 35
1.10 The Probability of a Union of Events 39
1.11 Statistical Swindles 45
1.12 Supplementary Exercises 47
^ Conditional Probability 49
2.1 The Definition of Conditional Probability 49
2.2 Independent Events 56
2.3 Bayes' Theorem 66
* 2.4 Markov Chains 79
* 2.5 The Gambler's Ruin Problem 89
2.6 Supplementary Exercises 93
Contents
3 Random Variables and Distributions 97
3.1 Random Variables and Discrete Distributions 97
3.2 Continuous Distributions 103
3.3 The Distribution Function 109
3.4 Bivariate Distributions 118
3.5 Marginal Distributions 128
3.6 Conditional Distributions 136
3.7 Multivariate Distributions 146
3.8 Functions of a Random Variable 158
3.9 Functions of Two or More Random Variables 165
3.10 Supplementary Exercises 176
4 Expectation isi
4.1 The Expectation of a Random Variable 181
4.2 Properties of Expectations 189
4.3 Variance 197
4.4 Moments 203
4.5 The Mean and the Median 209
4.6 Covariance and Correlation 214
4.7 Conditional Expectation 222
4.8 The Sample Mean 229
* 4.9 Utility 236
4.10 Supplementary Exercises 243
5 Special Distributions 247
5.1 Introduction 247
5.2 The Bernoulli and Binomial Distributions 247
5.3 The Hypergeometric Distribution 251
5.4 The Poisson Distribution 255
5.5 The Negative Binomial Distribution 263
5.6 The Normal Distribution 268
5.7 The Central Limit Theorem 282
5.8 The Correction for Continuity 291
5.9 The Gamma Distribution 295
5.10 The Beta Distribution 303
5.11 The Multinomial Distribution 309
5.12 The Bivariate Normal Distribution 313
5.13 Supplementary Exercises 320
Contents
O Estimation 323
6.1 Statistical Inference 323
6.2 Prior and Posterior Distributions 327
6.3 Conjugate Prior Distributions 335
6.4 Bayes Estimators 346
6.5 Maximum Likelihood Estimators 355
6.6 Properties of Maximum Likelihood Estimators 364
* 6.7 Sufficient Statistics 370
* 6.8 Jointly Sufficient Statistics 377
* 6.9 Improving an Estimator 383
6.10 Supplementary Exercises 389
/ Sampling Distributions of Estimators 391
7.1 The Sampling Distribution of a Statistic 391
7.2 The Chi Square Distribution 393
7.3 Joint Distribution of the Sample Mean and Sample Variance 39
7.4 The t Distribution 404
7.5 Confidence Intervals 409
*7.6 Bayesian Analysis of Samples from a Normal Distribution 416
7.7 Unbiased Estimators 427
* 7.8 Fisher Information 435
7.9 Supplementary Exercises 446
O Testing Hypotheses 449
8.1 Problems of Testing Hypotheses 449
* 8.2 Testing Simple Hypotheses 463
* 8.3 Uniformly Most Powerful Tests 470
* 8.4 Two Sided Alternatives 479
8.5 The t Test 485
8.6 Comparing the Means of Two Normal Distributions 498
8.7 The F Distribution 506
*8.8 Bayes Test Procedures 514
* 8.9 Foundational Issues 527
8.10 Supplementary Exercises 531
9 Categorical Data and Nonparametric Methods
9.1 Tests of Goodness of Fit 535
Contents
9.2 Goodness of Fit for Composite Hypotheses 542
9.3 Contingency Tables 550
9.4 Tests of Homogeneity 556
9.5 Simpson's Paradox 562
* 9.6 Kolmogorov Smirnov Tests 566
* 9.7 Robust Estimation 575
* 9.8 Sign and Rank Tests 587
9.9 Supplementary Exercises 595
10 Linear Statistical Models 599
10.1 The Method of Least Squares 599
10.2 Regression 609
10.3 Statistical Inference in Simple Linear Regression 618
* 10.4 Bayesian Inference in Simple Linear Regression 638
10.5 The General Linear Model and Multiple Regression 645
10.6 Analysis of Variance 665
* 10.7 The Two Way Layout 673
* 10.8 The Two Way Layout with Replications 683
10.9 Supplementary Exercises 694
X 1 Simulation 699
11.1 Why Is Simulation Useful? 699
11.2 Simulating Specific Distributions 713
11.3 Importance Sampling 727
* 11.4 Markov Chain Monte Carlo 735
11.5 The Bootstrap 753
11.6 Supplementary Exercises 765
Tables 769
Answers to Odd Numbered Exercises 781
References 801
Index 807 |
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| ctrlnum | (OCoLC)249250001 (DE-599)BVBBV022232608 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
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| id | DE-604.BV022232608 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:32:58Z |
| indexdate | 2024-07-09T20:52:57Z |
| institution | BVB |
| isbn | 0321204735 0201524880 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015443665 |
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| publishDate | 2002 |
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| series2 | Addison-Wesley series in statistics |
| spelling | DeGroot, Morris H. 1931-1989 Verfasser (DE-588)136916376 aut Probability and statistics Morris H. DeGroot 3. ed. Reading, Mass. u.a. Addison-Wesley 2002 XV, 816 S. Ill. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Statistik (DE-588)4056995-0 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 3\p DE-604 Schervish, Mark J. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015443665&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | DeGroot, Morris H. 1931-1989 Probability and statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4079013-7 (DE-588)4056995-0 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Probability and statistics |
| title_auth | Probability and statistics |
| title_exact_search | Probability and statistics |
| title_exact_search_txtP | Probability and statistics |
| title_full | Probability and statistics Morris H. DeGroot |
| title_fullStr | Probability and statistics Morris H. DeGroot |
| title_full_unstemmed | Probability and statistics Morris H. DeGroot |
| title_short | Probability and statistics |
| title_sort | probability and statistics |
| topic | Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Wahrscheinlichkeitsrechnung Wahrscheinlichkeitstheorie Statistik Einführung Lehrbuch |
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