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国外经典统计学习教材,Larsen and Marx,基本概念和实例讲解清楚,适合于自学。英文原版,有目录树!
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AN INTRODUCTION TO
MATHEMATICAL STATISTICS
AND
ITS APPLICATIONS
Fifth Edition
Richard J. Larsen
Vanderbilt University
Morris L. Marx
University of West Florida
Prentice Hall
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Production Coordination, Technical Illustrations, and Composition: Integra Software Services, Inc.
Cover Photo: © Jason Reed/Getty Images
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 was aware of a trademark
claim, the designations have been printed in initial caps or all caps.
Library of Congress Cataloging-in-Publication Data
Larsen, Richard J.
An introduction to mathematical statistics and its applications /
Richard J. Larsen, Morris L. Marx.—5th ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-321-69394-5
1. Mathematical statistics—Textbooks. I. Marx, Morris L. II. Title.
QA276.L314 2012
519.5—dc22
2010001387
Copyright © 2012, 2006, 2001, 1986, and 1981 by 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, 501 Boylston Street, Suite 900, Boston, MA 02116, fax your request
to 617-671-3447, or e-mail at http://www.pearsoned.com/legal/permissions.htm.
12345678910—EB—1413121110
ISBN-13: 978-0-321-69394-5
ISBN-10: 0-321-69394-9
Table of Contents
Preface viii
1
Introduction 1
1.1 An Overview 1
1.2 Some Examples 2
1.3 A Brief History 7
1.4 A Chapter Summary 14
2
Probability 16
2.1 Introduction 16
2.2 Sample Spaces and the Algebra of Sets 18
2.3 The Probability Function 27
2.4 Conditional Probability 32
2.5 Independence 53
2.6 Combinatorics 67
2.7 Combinatorial Probability 90
2.8 Taking a Second Look at Statistics (Monte Carlo Techniques) 99
3
Random Variables 102
3.1 Introduction 102
3.2 Binomial and Hypergeometric Probabilities 103
3.3 Discrete R andom Vari ables 118
3.4 Continuous Random Variables 129
3.5 Expected Values 139
3.6 The Variance 155
3.7 Joint Densities 162
3.8 Transforming and Combining Random Variables 176
3.9 Further Properties of the Mean and Variance 183
3.10 Order St atistics 193
3.11 Conditional Densities 200
3.12 Moment-Generating Functions 207
3.13 Taking a Second Look at Statistics (Interpreting Means) 216
Appendix 3.A.1 Minit ab Applications 218
iii
iv Table of Contents
4
Special Distributions 221
4.1 Introduction 221
4.2 The Poisson Distribution 222
4.3 The Normal Distribution 239
4.4 The Geometric Distribution 260
4.5 The Negative Binomial Distribution 262
4.6 The Gamma Distribution 270
4.7 Taking a Second Look at Statistics (Monte Carlo
Simulations)
274
Appendix 4.A.1 Minitab Applications 278
Appendix 4.A.2 A Proof of the Central Limit Theorem 280
5
Estimation 281
5.1 Introduction 281
5.2 Estimating Parameters: The Method of Maximum Likelihood and
the Method of Moments
284
5.3 Interval Estimation 297
5.4 Properties of Estimators 312
5.5 Minimum-Variance Estimators: The Cramér-Rao Lower
Bound
320
5.6 Sufficient Estimators 323
5.7 Consistency 330
5.8 Bayesian Estimation 333
5.9 Taking a Second Look at Statistics (Beyond Classical
Estimation)
345
Appendix 5.A.1 Minitab Applications 346
6
Hypothesis Testing 350
6.1 Introduction 350
6.2 The Decision Rule 351
6.3 Testing Binomial Data—H
0
: p = p
o
361
6.4 Type I and Type II Errors 366
6.5 A Notion of Optimality: The Generalized Likelihood Ratio 379
6.6 Taking a Second Look at Statistics (Statistical Significance versus
“Practical” Significance)
382
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