Probability & statistics for engineers & scientists

812 Pages·2017·8.577 MB·English

by  Walpole, Ronald E., Myers, Raymond H., Myers, Sharon L., Ye, Keying

Probability & Statistics for
Engineers & Scientists
N I N T H E D I T I O N
G L O B A L E D I T I O N
Ronald E. Walpole
Roanoke College
Raymond H. Myers
Virginia Tech
Sharon L. Myers
Radford University
Keying Ye
University of Texas at San Antonio
Boston Columbus Hoboken Indianapolis New York San Francisco
Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montr´eal Toronto
Delhi Mexico City Sa˜o Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
EditorialDirector: Chris Hoag Media Production Manager,GlobalEdition:
Editor in Chief: Deirdre Lynch Vikram Kumar
Acquisitions Editor: Patrick Barbera Media Producer: Aimee Thorne
MathXL Content Manager: Bob Carroll
Assistant Acquisitions Editor,GlobalEdition:
Product Marketing Manager: Tiffany Bitzel
Aditee Agarwal
Field Marketing Manager: Evan St. Cyr
EditorialAssistant: Justin Billing
Marketing Coordinator: Brooke Smith
Program Manager: Chere Bemelmans
Senior AuthorSupport/Technology Specialist: Joe Vetere
Project Manager: Christine Whitlock
Rights and Permissions Project Manager: Gina Cheselka
Program Management Team Lead: Karen Wernholm
Procurement Specialist: Carol Melville
Project Management Team Lead: Peter Silvia Associate Director ofDesign USHE EMSS/HSC/EDU:
Project Editor,GlobalEdition: K.K. Neelakantan Andrea Nix
Senior Manufacturing Controller,GlobalEdition: Program Design Lead: Heather Scott
Trudy Kimber CoverImage: ChillChillz / Shutterstock.com
Pearson Education Limited
Edinburgh Gate
Harlow
Essex CM20 2JE
England
and Associated Companies throughout the world
Visit us on the World Wide Web at: www.pearsonglobaleditions.com
(cid:2)c Pearson Education Limited 2016
TherightsofRonaldE.Walpole,RaymondH.Myers,SharonL.Myers,andKeyingYetobeidentifiedastheauthorsof
this work have been asserted by them in accordance with the Copyright,Designs and Patents Act 1988.
Authorized adaptation from the United States edition, entitled Probability & Statistics for Engineers & Scientists,9th
EditionMyStatLabUpdate,ISBN978-0-13-411585-6,byRonaldE.Walpole,RaymondH.Myers,SharonL.Myers,and
Keying Ye published by Pearson Education (cid:2)c 2017.
Acknowledgements ofthird party content appear on page 18,which constitutes an extension ofthis copyright page.
PEARSON,ALWAYSLEARNINGandMYSTATLABareexclusivetrademarksownedbyPearsonEducation,Inc. orits
affiliates in the U.S.and/or other countries.
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 either the prior written
permission of the publisher or a license permitting restricted copying in the United Kingdom issued by the Copyright
Licensing Agency Ltd,Saffron House,6−10 Kirby Street,London EC1N 8TS.
All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not
vestin the authororpublisherany trademark ownership rightsin such trademarks,nordoesthe use ofsuch trademarks
imply any affiliation with or endorsement ofthis book by such owners.
British Library Cataloguing-in-Publication Data
A catalogue record forthis book is available from the British Library
10 9 8 7 6 5 4 3 2 1
ISBN 10: 1292161361
ISBN 13: 9781292161365
Typeset by Aptara
Printed and bound in Italy by LEGO
This book is dedicated to
Billy and Julie
R.H.M. and S.L.M.
Limin, Carolyn and Emily
K.Y.
This page intentionally left blank
Contents
Preface .......................................................... 13
1 Introduction to Statistics and Data Analysis........... 21
1.1 Overview: Statistical Inference, Samples, Populations, and the
Role of Probability.............................................. 21
1.2 Sampling Procedures; Collection of Data........................ 27
1.3 Measures of Location: The Sample Mean and Median........... 31
Exercises................................................... 33
1.4 Measures of Variability.......................................... 34
Exercises................................................... 37
1.5 Discrete and Continuous Data................................... 37
1.6 Statistical Modeling, Scientific Inspection, and Graphical Diag-
nostics.......................................................... 38
1.7 General Types of Statistical Studies: Designed Experiment,
Observational Study, and Retrospective Study .................. 47
Exercises................................................... 50
2 Probability.................................................. 55
2.1 Sample Space................................................... 55
2.2 Events.......................................................... 58
Exercises................................................... 62
2.3 Counting Sample Points......................................... 64
Exercises................................................... 71
2.4 Probability of an Event......................................... 72
2.5 Additive Rules.................................................. 76
Exercises................................................... 79
2.6 Conditional Probability, Independence, and the Product Rule... 82
Exercises................................................... 89
2.7 Bayes’ Rule..................................................... 92
Exercises................................................... 96
Review Exercises............................................ 97
6 Contents
2.8 Potential Misconceptions and Hazards; Relationship to Material
in Other Chapters............................................... 99
3 Random Variables and Probability Distributions ...... 101
3.1 Concept of a Random Variable.................................. 101
3.2 Discrete Probability Distributions............................... 104
3.3 Continuous Probability Distributions............................ 107
Exercises................................................... 111
3.4 Joint Probability Distributions.................................. 114
Exercises................................................... 124
Review Exercises............................................ 127
3.5 Potential Misconceptions and Hazards; Relationship to Material
in Other Chapters............................................... 129
4 Mathematical Expectation................................ 131
4.1 Mean of a Random Variable..................................... 131
Exercises................................................... 137
4.2 Variance and Covariance of Random Variables................... 139
Exercises................................................... 147
4.3 MeansandVariancesofLinearCombinationsofRandomVariables 148
4.4 Chebyshev’s Theorem........................................... 155
Exercises................................................... 157
Review Exercises............................................ 159
4.5 Potential Misconceptions and Hazards; Relationship to Material
in Other Chapters............................................... 162
5 Some Discrete Probability Distributions................ 163
5.1 Introduction and Motivation.................................... 163
5.2 Binomial and Multinomial Distributions......................... 163
Exercises................................................... 170
5.3 Hypergeometric Distribution.................................... 172
Exercises................................................... 177
5.4 Negative Binomial and Geometric Distributions................. 178
5.5 Poisson Distribution and the Poisson Process.................... 181
Exercises................................................... 184
Review Exercises............................................ 186
5.6 Potential Misconceptions and Hazards; Relationship to Material
in Other Chapters............................................... 189
Contents 7
6 Some Continuous Probability Distributions............. 191
6.1 Continuous Uniform Distribution................................ 191
6.2 Normal Distribution............................................ 192
6.3 Areas under the Normal Curve.................................. 196
6.4 Applications of the Normal Distribution......................... 202
Exercises................................................... 205
6.5 Normal Approximation to the Binomial......................... 207
Exercises................................................... 213
6.6 Gamma and Exponential Distributions.......................... 214
6.7 Chi-Squared Distribution........................................ 220
6.8 Beta Distribution............................................... 221
6.9 Lognormal Distribution......................................... 221
6.10 Weibull Distribution (Optional)................................. 223
Exercises................................................... 226
Review Exercises............................................ 227
6.11 Potential Misconceptions and Hazards; Relationship to Material
in Other Chapters............................................... 229
7 Functions of Random Variables (Optional).............. 231
7.1 Introduction.................................................... 231
7.2 Transformations of Variables.................................... 231
7.3 Moments and Moment-Generating Functions.................... 238
Exercises................................................... 242
8 Fundamental Sampling Distributions and
Data Descriptions........................................ 245
8.1 Random Sampling.............................................. 245
8.2 Some Important Statistics....................................... 247
Exercises................................................... 250
8.3 Sampling Distributions.......................................... 252
8.4 Sampling Distribution of Means and the Central Limit Theorem. 253
Exercises................................................... 261
8.5 Sampling Distribution of S2..................................... 263
8.6 t-Distribution................................................... 266
8.7 F-Distribution.................................................. 271
8.8 Quantile and Probability Plots.................................. 274
Exercises................................................... 279
Review Exercises............................................ 280
8.9 Potential Misconceptions and Hazards; Relationship to Material
in Other Chapters............................................... 282
8 Contents
9 One- and Two-Sample Estimation Problems............ 285
9.1 Introduction.................................................... 285
9.2 Statistical Inference............................................. 285
9.3 Classical Methods of Estimation................................. 286
9.4 Single Sample: Estimating the Mean............................ 289
9.5 Standard Error of a Point Estimate............................. 296
9.6 Prediction Intervals............................................. 297
9.7 Tolerance Limits................................................ 300
Exercises................................................... 302
9.8 Two Samples: Estimating the Difference between Two Means... 305
9.9 Paired Observations............................................. 311
Exercises................................................... 314
9.10 Single Sample: Estimating a Proportion......................... 316
9.11 TwoSamples: EstimatingtheDifferencebetweenTwoProportions 320
Exercises................................................... 322
9.12 Single Sample: Estimating the Variance......................... 323
9.13 Two Samples: Estimating the Ratio of Two Variances........... 325
Exercises................................................... 327
9.14 Maximum Likelihood Estimation (Optional)..................... 327
Exercises................................................... 332
Review Exercises............................................ 333
9.15 Potential Misconceptions and Hazards; Relationship to Material
in Other Chapters............................................... 336
10 One- and Two-Sample Tests of Hypotheses............. 339
10.1 Statistical Hypotheses: General Concepts....................... 339
10.2 Testing a Statistical Hypothesis................................. 341
10.3 The Use of P-Values for Decision Making in Testing Hypotheses. 351
Exercises................................................... 354
10.4 Single Sample: Tests Concerning a Single Mean................. 356
10.5 Two Samples: Tests on Two Means............................. 362
10.6 Choice of Sample Size for Testing Means........................ 369
10.7 Graphical Methods for Comparing Means....................... 374
Exercises................................................... 376
10.8 One Sample: Test on a Single Proportion........................ 380
10.9 Two Samples: Tests on Two Proportions........................ 383
Exercises................................................... 385
10.10 One- and Two-Sample Tests Concerning Variances.............. 386
Exercises................................................... 389
10.11 Goodness-of-Fit Test............................................ 390
10.12 Test for Independence (Categorical Data)....................... 393
Contents 9
10.13 Test for Homogeneity........................................... 396
10.14 Two-Sample Case Study........................................ 399
Exercises................................................... 402
Review Exercises............................................ 404
10.15 Potential Misconceptions and Hazards; Relationship to Material
in Other Chapters............................................... 406
11 Simple Linear Regression and Correlation.............. 409
11.1 Introduction to Linear Regression............................... 409
11.2 The Simple Linear Regression Model............................ 410
11.3 Least Squares and the Fitted Model............................. 414
Exercises................................................... 418
11.4 Properties of the Least Squares Estimators...................... 420
11.5 Inferences Concerning the Regression Coefficients................ 423
11.6 Prediction...................................................... 428
Exercises................................................... 431
11.7 Choice of a Regression Model................................... 434
11.8 Analysis-of-Variance Approach.................................. 434
11.9 TestforLinearityofRegression: DatawithRepeatedObservations 436
Exercises................................................... 441
11.10 Data Plots and Transformations................................. 444
11.11 Simple Linear Regression Case Study............................ 448
11.12 Correlation ..................................................... 450
Exercises................................................... 455
Review Exercises............................................ 456
11.13 Potential Misconceptions and Hazards; Relationship to Material
in Other Chapters............................................... 462
12 Multiple Linear Regression and Certain
Nonlinear Regression Models........................... 463
12.1 Introduction.................................................... 463
12.2 Estimating the Coefficients...................................... 464
12.3 Linear Regression Model Using Matrices........................ 467
Exercises................................................... 470
12.4 Properties of the Least Squares Estimators...................... 473
12.5 Inferences in Multiple Linear Regression......................... 475
Exercises................................................... 481
12.6 Choice of a Fitted Model through Hypothesis Testing........... 482
12.7 Special Case of Orthogonality (Optional)........................ 487
Exercises................................................... 491
12.8 Categorical or Indicator Variables............................... 492