实例介绍
【实例简介】
概率论 UCLA研究生专用教材讲义 非常实用 如果有学有余力的本科生对于这个感兴趣也可以预习
Probability and statistics Fourth edition MORRIS H DEGROOT Carnegie Mellon university MARK J SCHERVISH Carnegie Mellon University Addison-Wesley Boston Columbus Indianapolis New York San Francisco Upper saddle river Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Editor in Chief: Deirdre Lynch Acquisitions Editor: Christopher Cummings Associate Content Editors: Leah Goldberg, Dana Jones Bettez Associate Editor: Christina Lepre Senior Managing Editor: Karen Wernholm Production Project Manager: Patty bergin Cover designer. heather scott Design Manager: Andrea nix g r. Alex g Marketing Assistant: Kathleen De Ch Senior Author Support/Technology Specialist: Joe Vetere Rights and Permissions Advisor: Michael Joyce Manufacturing Manager: Carol Melville Project Managernent, Composition. Windfall Software, using ZZTEX Cover Photo: Shutterstock/@ Marilyn volan The programs and applications presented in this book have been included for their instruc- tional value. They have been tested with care, but are not guaranteed for any particular purpose. The publisher does not offer any warranties or representations, nor does it accept any liabilities with respect to the programs or applications Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and Pearson education was aware of a trademark claim, the designations have been printed in initial caps or all caps Library of Congress Cataloging-in-Publication Data De groot morris h.1931-1989 Probability and statistics / Morris H. DeGroot, Mark J Schervish --4th ed p cm ISBN978-0-321-50046-5 1. Probabilities Textbooks. 2. Mathematical statistics Textbooks I Schervish. Mark. il. Title QA273D352012 5192-dc22 2010001486 Copyright O 2012, 2002 Pearson Education, Inc All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. For information on obtaining permission for use of material in this work please submit a written request to Pearson Education, Inc, Rights and Contracts Department, 75 Arlington Street, Suite 300, Boston, MA02116, fax your request to 617-848-7047, or e-mail athttp://www-pearsoned.com/legal/permissions.htm 12345678910EB-1413121110 Addison- wesley is an imprint of PEARSON ISBN10:0-321-50046-6 www.pearsonhighered.com ISBN13:978-0-32150046-5 o the memory of morrie Degroot MS This page intentionally left blank CONTENTS Prefa INTRODUCTION TO PROBABILITY 1 I I The History of Probability 1.2 Interpretations of Probability 2 1.3 Experiments and events 5 1. 4 Set Theory 6 1. 5 The Definition of probabilit 16 1.6 Finite Sample spac 22 1.7 Counting Method 1. 8 Combinatorial methods 32 1. 9 Multinomial Coefficients 42 1.Io The Probability of a union of Events 46 1.1 Statistical swindles 5 1.12 Supplementary Exercises 53 2 CONDITIONAL PROBABILITY 55 2. The definition of conditional probabilit 55 2.2 Independent events 2.3 bayes’ Theoren 76 *2.4 The Gambler's Ruin Problem 86 2.5 Supplementary Exercises RANDOM VARIABLES AND DISTRIBUTIONS 93 3.1 Random Variables and Discrete Distributions 93 3.2 Continuous distributions 100 3.3 The Cumulative distribution function 107 3.4 Bivariate Distributions |18 3.5 Marginal Distributions 130 3.6 Conditional Distributions 141 3.7 Multivariate Distributions 152 3. 8 Functions of a random variable 167 3. 9 Functions of Two or More Random variables 175 ★3. o Markov chains 188 3. 1 I Supplementary Exercises 202 vill Contents 4 Eⅹ PECTATION207 4.1 The Expectation of a Random variable 207 4.2 Properties of Expectations 217 4.3 Variance 225 4.4 Moments 234 4.5 The Mean and the median 24 4.6 Covariance and Correlation 248 4.7 Conditional Expectation 256 ★4.8 utility 265 4.9 Supplementary Exercises 272 SPECIAL DISTRIBUTIONS 275 troduction 275 5.2 The bernoulli and binomial distributions 275 5.3 The Hypergeometric Distributions 28 I 5.4 The Poisson Distributions 287 5.5 The Negative Binomial Distributions 297 5.6 The normal distributions 302 5.7 The Gamma Distributions 316 5. 8 The Beta distributions 27 5.9 The Multinomial Distributions 333 5.10 The Bivariate Normal Distributions 337 5. 11 Supplementary Exercises 345 6 LARGE RANDOM SAMPLES 347 6.1 Introduction 47 6.2 The Law of Large Numbers 348 6.3 The Central Limit theorem 360 6.4 The Correction for Continuity 371 6.5 Supplementary Exercises 375 ESTIMATION 376 7.1 Statistical Inference 376 7.2 Prior and Posterior Distributions 385 7.3 Conjugate Prior distributions 394 7. 4 Bayes Estimators 408 Contents 7.5 Maximum Likelihood Estimators 417 7.6 Properties of Maximum Likelihood Estimators 426 *7.7 Sufficient statistics 443 ★78」 ointly Sufficient Statistics449 *7.9 Improving an Estimator 455 7.10 Supplementary Exercises 461 SAMPLING DISTRIBUTIONS OF ESTIMATORS 464 8.1 The Sampling distribution of a Statistic 464 8.2 The Chi-Square Distributions 469 8.3 Joint Distribution of the Sample Mean and Sample variance 47 8.4 The t Distributions 480 8.5 Confidence Intervals 485 *8.6 Bayesian Analysis of Samples from a Normal Distribution495 8.7 Unbiased Estimators 506 *8.8 Fisher Information 514 8.9 Supplementary Exercises 528 TESTING HYPOTHESES 530 9.1 Problems of Testing Hypotheses 530 *9.2 Testing Simple Hypotheses 55 *9.3 Uniformly Most Powerful Tests 559 *9.4 Two-Sided Alternatives 567 9.5 The t Test 576 9.6 Comparing the means of Two Normal Distributions 587 9.7 The F Distributions 597 *9.8 bayes Test procedures 605 9.9 Foundational Issues 617 9.10 Supplementary Exercises 621 10 CATEGORICAL DATA AND NONPARAMETRIC METHODS 624 10.1 Tests of Goodness-of-Fit 624 10.2 Goodness-of-Fit for Composite Hypotheses 633 10.3 Contingency Tables 64 I 10.4 Tests of Homogeneity 647 10.5 Simpsons Paradox 653 10.6 Kolmogorov-Smirnov Tests 657 x Contents * 10.7 Robust estimation 666 10 8 Sign and Rank Tests 678 10.9 Supplementary Exercises 686 11 LINEAR STATISTICAL MODELS 689 I 1. The Method of Least Squares 689 2 Regression 698 1 1.3 Statistical Inference in Simple Linear Regression 707 11 4 Bayesian Inference in Simple Linear Regression 729 1 1.5 The General Linear Model and Multiple Regression 736 11. 6 Analysis of Variance 754 ★I7 The Two-Way layout 763 *11. 8 The Two-Way layout with replications 772 1 1.9 Supplementary Exercises 783 12S IMULATION 787 12.1 What Is Simulation? 787 12.2 Why Is simulation useful? 79 1 12.3 Simulating Specific Distributions 804 12. 4 Importance Sampling 816 *12.5 Markov Chain monte carlo 823 12.6 The bootstrap 839 12.7 Supplementary Exercises 850 Tables 853 Answers to odd-Numbered Exercises 865 References 879 ex 885 【实例截图】
【核心代码】
概率论 UCLA研究生专用教材讲义 非常实用 如果有学有余力的本科生对于这个感兴趣也可以预习
Probability and statistics Fourth edition MORRIS H DEGROOT Carnegie Mellon university MARK J SCHERVISH Carnegie Mellon University Addison-Wesley Boston Columbus Indianapolis New York San Francisco Upper saddle river Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Editor in Chief: Deirdre Lynch Acquisitions Editor: Christopher Cummings Associate Content Editors: Leah Goldberg, Dana Jones Bettez Associate Editor: Christina Lepre Senior Managing Editor: Karen Wernholm Production Project Manager: Patty bergin Cover designer. heather scott Design Manager: Andrea nix g r. Alex g Marketing Assistant: Kathleen De Ch Senior Author Support/Technology Specialist: Joe Vetere Rights and Permissions Advisor: Michael Joyce Manufacturing Manager: Carol Melville Project Managernent, Composition. Windfall Software, using ZZTEX Cover Photo: Shutterstock/@ Marilyn volan The programs and applications presented in this book have been included for their instruc- tional value. They have been tested with care, but are not guaranteed for any particular purpose. The publisher does not offer any warranties or representations, nor does it accept any liabilities with respect to the programs or applications Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and Pearson education was aware of a trademark claim, the designations have been printed in initial caps or all caps Library of Congress Cataloging-in-Publication Data De groot morris h.1931-1989 Probability and statistics / Morris H. DeGroot, Mark J Schervish --4th ed p cm ISBN978-0-321-50046-5 1. Probabilities Textbooks. 2. Mathematical statistics Textbooks I Schervish. Mark. il. Title QA273D352012 5192-dc22 2010001486 Copyright O 2012, 2002 Pearson Education, Inc All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. For information on obtaining permission for use of material in this work please submit a written request to Pearson Education, Inc, Rights and Contracts Department, 75 Arlington Street, Suite 300, Boston, MA02116, fax your request to 617-848-7047, or e-mail athttp://www-pearsoned.com/legal/permissions.htm 12345678910EB-1413121110 Addison- wesley is an imprint of PEARSON ISBN10:0-321-50046-6 www.pearsonhighered.com ISBN13:978-0-32150046-5 o the memory of morrie Degroot MS This page intentionally left blank CONTENTS Prefa INTRODUCTION TO PROBABILITY 1 I I The History of Probability 1.2 Interpretations of Probability 2 1.3 Experiments and events 5 1. 4 Set Theory 6 1. 5 The Definition of probabilit 16 1.6 Finite Sample spac 22 1.7 Counting Method 1. 8 Combinatorial methods 32 1. 9 Multinomial Coefficients 42 1.Io The Probability of a union of Events 46 1.1 Statistical swindles 5 1.12 Supplementary Exercises 53 2 CONDITIONAL PROBABILITY 55 2. The definition of conditional probabilit 55 2.2 Independent events 2.3 bayes’ Theoren 76 *2.4 The Gambler's Ruin Problem 86 2.5 Supplementary Exercises RANDOM VARIABLES AND DISTRIBUTIONS 93 3.1 Random Variables and Discrete Distributions 93 3.2 Continuous distributions 100 3.3 The Cumulative distribution function 107 3.4 Bivariate Distributions |18 3.5 Marginal Distributions 130 3.6 Conditional Distributions 141 3.7 Multivariate Distributions 152 3. 8 Functions of a random variable 167 3. 9 Functions of Two or More Random variables 175 ★3. o Markov chains 188 3. 1 I Supplementary Exercises 202 vill Contents 4 Eⅹ PECTATION207 4.1 The Expectation of a Random variable 207 4.2 Properties of Expectations 217 4.3 Variance 225 4.4 Moments 234 4.5 The Mean and the median 24 4.6 Covariance and Correlation 248 4.7 Conditional Expectation 256 ★4.8 utility 265 4.9 Supplementary Exercises 272 SPECIAL DISTRIBUTIONS 275 troduction 275 5.2 The bernoulli and binomial distributions 275 5.3 The Hypergeometric Distributions 28 I 5.4 The Poisson Distributions 287 5.5 The Negative Binomial Distributions 297 5.6 The normal distributions 302 5.7 The Gamma Distributions 316 5. 8 The Beta distributions 27 5.9 The Multinomial Distributions 333 5.10 The Bivariate Normal Distributions 337 5. 11 Supplementary Exercises 345 6 LARGE RANDOM SAMPLES 347 6.1 Introduction 47 6.2 The Law of Large Numbers 348 6.3 The Central Limit theorem 360 6.4 The Correction for Continuity 371 6.5 Supplementary Exercises 375 ESTIMATION 376 7.1 Statistical Inference 376 7.2 Prior and Posterior Distributions 385 7.3 Conjugate Prior distributions 394 7. 4 Bayes Estimators 408 Contents 7.5 Maximum Likelihood Estimators 417 7.6 Properties of Maximum Likelihood Estimators 426 *7.7 Sufficient statistics 443 ★78」 ointly Sufficient Statistics449 *7.9 Improving an Estimator 455 7.10 Supplementary Exercises 461 SAMPLING DISTRIBUTIONS OF ESTIMATORS 464 8.1 The Sampling distribution of a Statistic 464 8.2 The Chi-Square Distributions 469 8.3 Joint Distribution of the Sample Mean and Sample variance 47 8.4 The t Distributions 480 8.5 Confidence Intervals 485 *8.6 Bayesian Analysis of Samples from a Normal Distribution495 8.7 Unbiased Estimators 506 *8.8 Fisher Information 514 8.9 Supplementary Exercises 528 TESTING HYPOTHESES 530 9.1 Problems of Testing Hypotheses 530 *9.2 Testing Simple Hypotheses 55 *9.3 Uniformly Most Powerful Tests 559 *9.4 Two-Sided Alternatives 567 9.5 The t Test 576 9.6 Comparing the means of Two Normal Distributions 587 9.7 The F Distributions 597 *9.8 bayes Test procedures 605 9.9 Foundational Issues 617 9.10 Supplementary Exercises 621 10 CATEGORICAL DATA AND NONPARAMETRIC METHODS 624 10.1 Tests of Goodness-of-Fit 624 10.2 Goodness-of-Fit for Composite Hypotheses 633 10.3 Contingency Tables 64 I 10.4 Tests of Homogeneity 647 10.5 Simpsons Paradox 653 10.6 Kolmogorov-Smirnov Tests 657 x Contents * 10.7 Robust estimation 666 10 8 Sign and Rank Tests 678 10.9 Supplementary Exercises 686 11 LINEAR STATISTICAL MODELS 689 I 1. The Method of Least Squares 689 2 Regression 698 1 1.3 Statistical Inference in Simple Linear Regression 707 11 4 Bayesian Inference in Simple Linear Regression 729 1 1.5 The General Linear Model and Multiple Regression 736 11. 6 Analysis of Variance 754 ★I7 The Two-Way layout 763 *11. 8 The Two-Way layout with replications 772 1 1.9 Supplementary Exercises 783 12S IMULATION 787 12.1 What Is Simulation? 787 12.2 Why Is simulation useful? 79 1 12.3 Simulating Specific Distributions 804 12. 4 Importance Sampling 816 *12.5 Markov Chain monte carlo 823 12.6 The bootstrap 839 12.7 Supplementary Exercises 850 Tables 853 Answers to odd-Numbered Exercises 865 References 879 ex 885 【实例截图】
【核心代码】
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