ProbabilityandStatistics(4thEdition)

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 statisticsFourth editionMORRIS H DEGROOTCarnegie Mellon universityMARK J SCHERVISHCarnegie Mellon UniversityAddison-WesleyBoston Columbus Indianapolis New York San Francisco Upper saddle riverAmsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal TorontoDelhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei TokyoEditor in Chief: Deirdre LynchAcquisitions Editor: Christopher CummingsAssociate Content Editors: Leah Goldberg, Dana Jones BettezAssociate Editor: Christina LepreSenior Managing Editor: Karen WernholmProduction Project Manager: Patty berginCover designer. heather scottDesign Manager: Andrea nixgr. Alex gMarketing Assistant: Kathleen De ChSenior Author Support/Technology Specialist: Joe VetereRights and Permissions Advisor: Michael JoyceManufacturing Manager: Carol MelvilleProject Managernent, Composition. Windfall Software, using ZZTEXCover Photo: Shutterstock/@ Marilyn volanThe 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 particularpurpose. The publisher does not offer any warranties or representations, nor does it acceptany liabilities with respect to the programs or applicationsMany of the designations used by manufacturers and sellers to distinguish their products areclaimed as trademarks. Where those designations appear in this book, and Pearson educationwas aware of a trademark claim, the designations have been printed in initial caps or all capsLibrary of Congress Cataloging-in-Publication DataDe groot morris h.1931-1989Probability and statistics / Morris H. DeGroot, Mark J Schervish --4th edpcmISBN978-0-321-50046-51. Probabilities Textbooks. 2. Mathematical statistics TextbooksI Schervish. Mark. il. TitleQA273D3520125192-dc222010001486Copyright O 2012, 2002 Pearson Education, IncAll rights reserved. No part of this publication may be reproduced, stored in a retrieval systemor 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 UnitedStates of America. For information on obtaining permission for use of material in this workplease 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-mailathttp://www-pearsoned.com/legal/permissions.htm12345678910EB-1413121110Addison- wesleyis an imprint ofPEARSONISBN10:0-321-50046-6www.pearsonhighered.comISBN13:978-0-32150046-5o the memory of morrie DegrootMSThis page intentionally left blankCONTENTSPrefaINTRODUCTION TO PROBABILITY 1I I The History of Probability1.2 Interpretations of Probability 21.3 Experiments and events 51. 4 Set Theory 61. 5 The Definition of probabilit161.6 Finite Sample spac221.7 Counting Method1. 8 Combinatorial methods 321. 9 Multinomial Coefficients 421.Io The Probability of a union of Events 461.1 Statistical swindles 51.12 Supplementary Exercises 532CONDITIONAL PROBABILITY 552. The definition of conditional probabilit552.2 Independent events2.3 bayes’ Theoren76*2.4 The Gambler's Ruin Problem 862.5 Supplementary ExercisesRANDOM VARIABLES AND DISTRIBUTIONS 933.1 Random Variables and Discrete Distributions 933.2 Continuous distributions 1003.3 The Cumulative distribution function1073.4 Bivariate Distributions |183.5 Marginal Distributions1303.6 Conditional Distributions 1413.7 Multivariate Distributions 1523. 8 Functions of a random variable1673. 9 Functions of Two or More Random variables 175★3. o Markov chains1883. 1 I Supplementary Exercises 202vill Contents4Eⅹ PECTATION2074.1 The Expectation of a Random variable 2074.2 Properties of Expectations 2174.3 Variance 2254.4 Moments 2344.5 The Mean and the median 244.6 Covariance and Correlation 2484.7 Conditional Expectation 256★4.8 utility2654.9 Supplementary Exercises 272SPECIAL DISTRIBUTIONS 275troduction 2755.2 The bernoulli and binomial distributions 2755.3 The Hypergeometric Distributions 28 I5.4 The Poisson Distributions 2875.5 The Negative Binomial Distributions 2975.6 The normal distributions 3025.7 The Gamma Distributions 3165. 8 The Beta distributions275.9 The Multinomial Distributions 3335.10 The Bivariate Normal Distributions 3375. 11 Supplementary Exercises 3456LARGE RANDOM SAMPLES 3476.1 Introduction476.2 The Law of Large Numbers 3486.3 The Central Limit theorem 3606.4 The Correction for Continuity 3716.5 Supplementary Exercises 375ESTIMATION 3767.1 Statistical Inference 3767.2 Prior and Posterior Distributions 3857.3 Conjugate Prior distributions3947. 4 Bayes Estimators 408Contents7.5 Maximum Likelihood Estimators 4177.6 Properties of Maximum Likelihood Estimators 426*7.7 Sufficient statistics 443★78」 ointly Sufficient Statistics449*7.9 Improving an Estimator 4557.10 Supplementary Exercises 461SAMPLING DISTRIBUTIONS OF ESTIMATORS 4648.1 The Sampling distribution of a Statistic 4648.2 The Chi-Square Distributions 4698.3 Joint Distribution of the Sample Mean and Sample variance 478.4 The t Distributions 4808.5 Confidence Intervals 485*8.6 Bayesian Analysis of Samples from a Normal Distribution4958.7 Unbiased Estimators 506*8.8 Fisher Information 5148.9 Supplementary Exercises 528TESTING HYPOTHESES 5309.1 Problems of Testing Hypotheses 530*9.2 Testing Simple Hypotheses 55*9.3 Uniformly Most Powerful Tests 559*9.4 Two-Sided Alternatives 5679.5 The t Test 5769.6 Comparing the means of Two Normal Distributions 5879.7 The F Distributions 597*9.8 bayes Test procedures 6059.9 Foundational Issues 6179.10 Supplementary Exercises 62110 CATEGORICAL DATA AND NONPARAMETRIC METHODS 62410.1 Tests of Goodness-of-Fit 62410.2 Goodness-of-Fit for Composite Hypotheses 63310.3 Contingency Tables 64 I10.4 Tests of Homogeneity 64710.5 Simpsons Paradox65310.6 Kolmogorov-Smirnov Tests 657x Contents* 10.7 Robust estimation 66610 8 Sign and Rank Tests 67810.9 Supplementary Exercises 68611 LINEAR STATISTICAL MODELS 689I 1. The Method of Least Squares6892Regression6981 1.3 Statistical Inference in Simple Linear Regression 70711 4 Bayesian Inference in Simple Linear Regression 7291 1.5 The General Linear Model and Multiple Regression 73611. 6 Analysis of Variance 754★I7 The Two-Way layout763*11. 8 The Two-Way layout with replications 7721 1.9 Supplementary Exercises 78312SIMULATION78712.1 What Is Simulation? 78712.2 Why Is simulation useful? 79 112.3 Simulating Specific Distributions 80412. 4 Importance Sampling 816*12.5 Markov Chain monte carlo 82312.6 The bootstrap83912.7 Supplementary Exercises 850Tables 853Answers to odd-Numbered Exercises 865References 879ex885