Probability and Statistics for Engineers and Scientists

848 Pages·2012·35.02 MB·English

by  Anthony J. Hayter

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Probability and Statistics
for Engineers and
Scientists
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Probability and Statistics
for Engineers and
Scientists
FOURTH EDITION
Anthony Hayter
University of Denver
Australia•Brazil•Japan•Korea•Mexico•Singapore• Spain•UnitedKingdom•UnitedStates
iii
ProbabilityandStatisticsforEngineers ©2012Brooks/Cole,CengageLearning
andScientists,FourthEdition
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AnthonyHayter
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ABOUT THE AUTHOR
Dr.AnthonyHayterobtainedatriplefirst-classdegreeinmathematicsfromCambridge
UniversityinEnglandandaPh.D.instatisticsfromCornellUniversity.Hisdoctoralthesis
includedtheproofofafamousmathematicalconjecturethathadremainedunsolvedfor
thirtyyears,andheistheauthorofnumerousresearchpublicationsinthefieldsof
experimentaldesignandapplieddataanalysis.
Dr.Hayterispassionateaboutempoweringstudentsandresearcherswiththeskillsand
knowledgethattheyneedtoperformeffectiveandaccuratedataanalysis.Withhis
experienceasateacher,researcher,andconsultantinawidevarietyofsettings,Dr.Hayter
knowshowessentialtheseskillsareintoday’sworkplace.Dr.Hayter’sworkhasshownhim
thesubstantialadvantagesthataccruefromaclearunderstandingoftheconceptsof
probabilityandstatistics,togetherwiththepitfallsthatcanarisefromtheirmisuse.
Dr.Haytercollaboratesonmanyresearchprojects,includingworktoimprove
wheelchairdesignsandtoprovidebetterassistivetechnologiestodisabledpeople.Hehas
servedasasitereviewteammemberattheNationalInstitutesofHealth.Inaddition,hehas
workedonprojectstoimprovethesafetyofbridges,tomonitorairpollutionlevels,andto
promoteequitabletaxationrates,alongwithvariousotherprojectsthatareusedasexamples
anddatasetsinthistextbook.Dr.Hayterhasbeenakeynotespeakeratinternationalresearch
conferences,andhasbeenapanelistatsymposiaonbusinessinformationandanalytics.
HehasbeenaninvitedresearcheratuniversitiesinEngland,Japan,HongKongand
Singapore,andhehasreceivedaFulbrightScholarshiptoassistthegovernmentand
businessesinThailandwithdatacollectionandanalysis.
Inhissparetime,Dr.HayterlikestoreadthedetectivestoriesofTimothyHemion.In
fact,Dr.Haytertellshisstudentsthatconductingagooddataanalysisislikebeingpart
ofadetectivestory.Awell-designedexperimentprovidespertinentevidence,andthe
statistician’sjobistoknowhowtoextracttherelevantcluesfromthedataset.Theseclues
canthenbeusedtopiecetogetherapictureofthetruestateofaffairs,andtheymaybe
usedtodisproveorsubstantiatethetheoriesandhypothesesthathavebeenputforward.
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CONTENTS
Preface x 3.3 TheHypergeometricDistribution 168
3.4 ThePoissonDistribution 173
ContinuingCaseStudies:MicroelectronicSolderJoints
3.5 TheMultinomialDistribution 179
andInternetMarketing xv
3.6 CaseStudy:Microelectronic
SolderJoints 183
CHAPTER 1
3.7 CaseStudy:InternetMarketing 184
PROBABILITY THEORY 1
3.8 SupplementaryProblems 184
1.1 Probabilities 1
1.2 Events 8 CHAPTER 4
1.3 CombinationsofEvents 15 CONTINUOUS PROBABILITY
1.4 ConditionalProbability 33
DISTRIBUTIONS 186
1.5 ProbabilitiesofEventIntersections 40
1.6 PosteriorProbabilities 50
4.1 TheUniformDistribution 186
1.7 CountingTechniques 56
4.2 TheExponentialDistribution 190
1.8 CaseStudy:MicroelectronicSolderJoints 64
4.3 TheGammaDistribution 199
1.9 CaseStudy:InternetMarketing 66
4.4 TheWeibullDistribution 204
1.10 SupplementaryProblems 66
4.5 TheBetaDistribution 209
CHAPTER 2 4.6 CaseStudy:Microelectronic
SolderJoints 213
RANDOM VARIABLES 71
4.7 CaseStudy:InternetMarketing 213
4.8 SupplementaryProblems 214
2.1 DiscreteRandomVariables 71
2.2 ContinuousRandomVariables 81
2.3 TheExpectationofaRandomVariable 93 CHAPTER 5
2.4 TheVarianceofaRandomVariable 102 THE NORMAL DISTRIBUTION 216
2.5 JointlyDistributedRandomVariables 114
2.6 CombinationsandFunctions
5.1 ProbabilityCalculationsUsingthe
ofRandomVariables 129
NormalDistribution 216
2.7 CaseStudy:MicroelectronicSolderJoints 142
5.2 LinearCombinationsofNormal
2.8 CaseStudy:InternetMarketing 143
RandomVariables 229
2.9 SupplementaryProblems 143
5.3 ApproximatingDistributionswiththe
NormalDistribution 240
CHAPTER 3
5.4 DistributionsRelatedtothe
DISCRETE PROBABILITY NormalDistribution 251
DISTRIBUTIONS 147 5.5 CaseStudy:Microelectronic
SolderJoints 262
3.1 TheBinomialDistribution 147 5.6 CaseStudy:InternetMarketing 263
3.2 TheGeometricandNegative 5.7 SupplementaryProblems 263
BinomialDistributions 160
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Hayter-1140033 27044˙00˙fm September8,2011 9:36
viii CONTENTS
CHAPTER 6 9.5 CaseStudy:MicroelectronicSolderJoints 424
DESCRIPTIVE STATISTICS 267 9.6 CaseStudy:InternetMarketing 426
9.7 SupplementaryProblems 427
6.1 Experimentation 267
6.2 DataPresentation 272 CHAPTER 10
6.3 SampleStatistics 280 DISCRETE DATA ANALYSIS 432
6.4 Examples 288
6.5 CaseStudy:MicroelectronicSolderJoints 292
10.1 InferencesonaPopulationProportion 432
6.6 CaseStudy:InternetMarketing 293
10.2 ComparingTwoPopulationProportions 455
6.7 SupplementaryProblems 293
10.3 GoodnessofFitTestsforOne-Way
ContingencyTables 466
CHAPTER 7 10.4 TestingforIndependenceinTwo-Way
STATISTICAL ESTIMATION AND ContingencyTables 478
10.5 CaseStudy:MicroelectronicSolderJoints 488
SAMPLING DISTRIBUTIONS 296
10.6 CaseStudy:InternetMarketing 489
10.7 SupplementaryProblems 490
7.1 PointEstimates 296
7.2 PropertiesofPointEstimates 301
CHAPTER 11
7.3 SamplingDistributions 311
7.4 ConstructingParameterEstimates 320 THE ANALYSIS OF VARIANCE 494
7.5 CaseStudy:MicroelectronicSolderJoints 327
7.6 CaseStudy:InternetMarketing 327 11.1 One-FactorAnalysisofVariance 494
7.7 SupplementaryProblems 327 11.2 RandomizedBlockDesigns 520
11.3 CaseStudy:MicroelectronicSolderJoints 537
GuidetoStatisticalInferenceMethodologies
11.4 CaseStudy:InternetMarketing 539
11.5 SupplementaryProblems 540
CHAPTER 8
INFERENCES ON A CHAPTER 12
POPULATION MEAN 333 SIMPLE LINEAR REGRESSION
AND CORRELATION 543
8.1 ConfidenceIntervals 333
8.2 HypothesisTesting 349
12.1 TheSimpleLinearRegressionModel 543
8.3 Summary 381
12.2 FittingtheRegressionLine 551
8.4 CaseStudy:MicroelectronicSolderJoints 383
12.3 InferencesontheSlopeParameterβ 561
8.5 CaseStudy:InternetMarketing 384 1
12.4 InferencesontheRegressionLine 569
8.6 SupplementaryProblems 384
12.5 PredictionIntervalsforFuture
ResponseValues 575
CHAPTER 9 12.6 TheAnalysisofVarianceTable 579
COMPARING TWO 12.7 ResidualAnalysis 585
POPULATION MEANS 389 12.8 VariableTransformations 590
12.9 CorrelationAnalysis 594
12.10CaseStudy:MicroelectronicSolder
9.1 Introduction 389
Joints 600
9.2 AnalysisofPairedSamples 397
12.11CaseStudy:InternetMarketing 601
9.3 AnalysisofIndependentSamples 402
12.12SupplementaryProblems 602
9.4 Summary 422