,PROBABILITY AND STATISTICAL INFERENCE
Ninth Edition
Robert V. Hogg
Elliot A. Tanis
Dale L. Zimmerman
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
Sponsoring Editor: Christina Lepre
Assistant Editor: Sonia Ashraf
Marketing Manager: Erin Lane
Marketing Assistant: Kathleen DeChavez
Senior Managing Editor: Karen Wernholm
Senior Production Editor: Beth Houston
Procurement Manager: Vincent Scelta
Procurement Specialist: Carol Melville
Associate Director of Design, USHE EMSS/HSC/EDU: Andrea Nix
Art Director: Heather Scott
Interior Designer: Tamara Newnam
Cover Designer: Heather Scott
Cover Image: Agsandrew/Shutterstock
Full-Service Project Management: Integra Software Services
Composition: Integra Software Services
Copyright c 2015, 2010, 2006 by Pearson Education, Inc. All rights reserved. Manufactured
in the United States of America. This publication is protected by Copyright, and permission
should be obtained from the publisher prior to any prohibited reproduction, storage in a
retrieval system, or transmission in any form or by any means, electronic, mechanical,
photocopying, recording, or likewise. To obtain permission(s) to use material from this work,
please submit a written request to Pearson Higher Education, Rights and Contracts
Department, One Lake Street, Upper Saddle River, NJ 07458, or fax your request to
201-236-3290.
Many of the designations by manufacturers and seller to distinguish their products are
claimed as trademarks. Where those designations appear in this book, and the publisher was
aware of a trademark claim, the designations have been printed in initial caps or all caps.
Library of Congress Cataloging-in-Publication Data
Hogg, Robert V.
Probability and Statistical Inference/
Robert V. Hogg, Elliot A. Tanis, Dale Zimmerman. – 9th ed.
p. cm.
ISBN 978-0-321-92327-1
1. Mathematical statistics. I. Hogg, Robert V., II. Tanis, Elliot A. III. Title.
QA276.H59 2013
519.5–dc23
2011034906
10 9 8 7 6 5 4 3 2 1 EBM 17 16 15 14 13
ISBN-10: 0-321-92327-8
www.pearsonhighered.com ISBN-13: 978-0-321-92327-1
, Contents
Preface v
5 Distributions of Functions
of Random Variables 163
Prologue vii
5.1 Functions of One Random Variable 163
1 Probability 1 5.2 Transformations of Two Random
Variables 171
1.1 Properties of Probability 1
5.3 Several Random Variables 180
1.2 Methods of Enumeration 11
5.4 The Moment-Generating Function
1.3 Conditional Probability 20 Technique 187
1.4 Independent Events 29 5.5 Random Functions Associated with Normal
1.5 Bayes’ Theorem 35 Distributions 192
5.6 The Central Limit Theorem 200
2 Discrete Distributions 41 5.7 Approximations for Discrete
Distributions 206
2.1 Random Variables of the Discrete Type 41 5.8 Chebyshev’s Inequality and Convergence
2.2 Mathematical Expectation 49 in Probability 213
2.3 Special Mathematical Expectations 56 5.9 Limiting Moment-Generating Functions 217
2.4 The Binomial Distribution 65
2.5
2.6
The Negative Binomial Distribution 74
The Poisson Distribution 79
6 Point Estimation 225
6.1 Descriptive Statistics 225
6.2 Exploratory Data Analysis 238
3 Continuous Distributions 87
6.3 Order Statistics 248
3.1 Random Variables of the Continuous 6.4 Maximum Likelihood Estimation 256
Type 87
6.5 A Simple Regression Problem 267
3.2 The Exponential, Gamma, and Chi-Square
Distributions 95 6.6* Asymptotic Distributions of Maximum
Likelihood Estimators 275
3.3 The Normal Distribution 105
6.7 Sufficient Statistics 280
3.4* Additional Models 114
6.8 Bayesian Estimation 288
6.9* More Bayesian Concepts 294
4 Bivariate Distributions 125
4.1 Bivariate Distributions of the Discrete
Type 125 7 Interval Estimation 301
4.2 The Correlation Coefficient 134 7.1 Confidence Intervals for Means 301
4.3 Conditional Distributions 140 7.2 Confidence Intervals for the Difference
4.4 Bivariate Distributions of the Continuous of Two Means 308
Type 146 7.3 Confidence Intervals for Proportions 318
4.5 The Bivariate Normal Distribution 155 7.4 Sample Size 324
iii
Ninth Edition
Robert V. Hogg
Elliot A. Tanis
Dale L. Zimmerman
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
Sponsoring Editor: Christina Lepre
Assistant Editor: Sonia Ashraf
Marketing Manager: Erin Lane
Marketing Assistant: Kathleen DeChavez
Senior Managing Editor: Karen Wernholm
Senior Production Editor: Beth Houston
Procurement Manager: Vincent Scelta
Procurement Specialist: Carol Melville
Associate Director of Design, USHE EMSS/HSC/EDU: Andrea Nix
Art Director: Heather Scott
Interior Designer: Tamara Newnam
Cover Designer: Heather Scott
Cover Image: Agsandrew/Shutterstock
Full-Service Project Management: Integra Software Services
Composition: Integra Software Services
Copyright c 2015, 2010, 2006 by Pearson Education, Inc. All rights reserved. Manufactured
in the United States of America. This publication is protected by Copyright, and permission
should be obtained from the publisher prior to any prohibited reproduction, storage in a
retrieval system, or transmission in any form or by any means, electronic, mechanical,
photocopying, recording, or likewise. To obtain permission(s) to use material from this work,
please submit a written request to Pearson Higher Education, Rights and Contracts
Department, One Lake Street, Upper Saddle River, NJ 07458, or fax your request to
201-236-3290.
Many of the designations by manufacturers and seller to distinguish their products are
claimed as trademarks. Where those designations appear in this book, and the publisher was
aware of a trademark claim, the designations have been printed in initial caps or all caps.
Library of Congress Cataloging-in-Publication Data
Hogg, Robert V.
Probability and Statistical Inference/
Robert V. Hogg, Elliot A. Tanis, Dale Zimmerman. – 9th ed.
p. cm.
ISBN 978-0-321-92327-1
1. Mathematical statistics. I. Hogg, Robert V., II. Tanis, Elliot A. III. Title.
QA276.H59 2013
519.5–dc23
2011034906
10 9 8 7 6 5 4 3 2 1 EBM 17 16 15 14 13
ISBN-10: 0-321-92327-8
www.pearsonhighered.com ISBN-13: 978-0-321-92327-1
, Contents
Preface v
5 Distributions of Functions
of Random Variables 163
Prologue vii
5.1 Functions of One Random Variable 163
1 Probability 1 5.2 Transformations of Two Random
Variables 171
1.1 Properties of Probability 1
5.3 Several Random Variables 180
1.2 Methods of Enumeration 11
5.4 The Moment-Generating Function
1.3 Conditional Probability 20 Technique 187
1.4 Independent Events 29 5.5 Random Functions Associated with Normal
1.5 Bayes’ Theorem 35 Distributions 192
5.6 The Central Limit Theorem 200
2 Discrete Distributions 41 5.7 Approximations for Discrete
Distributions 206
2.1 Random Variables of the Discrete Type 41 5.8 Chebyshev’s Inequality and Convergence
2.2 Mathematical Expectation 49 in Probability 213
2.3 Special Mathematical Expectations 56 5.9 Limiting Moment-Generating Functions 217
2.4 The Binomial Distribution 65
2.5
2.6
The Negative Binomial Distribution 74
The Poisson Distribution 79
6 Point Estimation 225
6.1 Descriptive Statistics 225
6.2 Exploratory Data Analysis 238
3 Continuous Distributions 87
6.3 Order Statistics 248
3.1 Random Variables of the Continuous 6.4 Maximum Likelihood Estimation 256
Type 87
6.5 A Simple Regression Problem 267
3.2 The Exponential, Gamma, and Chi-Square
Distributions 95 6.6* Asymptotic Distributions of Maximum
Likelihood Estimators 275
3.3 The Normal Distribution 105
6.7 Sufficient Statistics 280
3.4* Additional Models 114
6.8 Bayesian Estimation 288
6.9* More Bayesian Concepts 294
4 Bivariate Distributions 125
4.1 Bivariate Distributions of the Discrete
Type 125 7 Interval Estimation 301
4.2 The Correlation Coefficient 134 7.1 Confidence Intervals for Means 301
4.3 Conditional Distributions 140 7.2 Confidence Intervals for the Difference
4.4 Bivariate Distributions of the Continuous of Two Means 308
Type 146 7.3 Confidence Intervals for Proportions 318
4.5 The Bivariate Normal Distribution 155 7.4 Sample Size 324
iii
