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1、Chapter6-LearningObjectivesDistinguishbetweendiscreteandcontinuousrandomvariables.DifferentiatebetweenthebinomialandthePoissondiscreteprobabilitydistributionsandtheirapplications.Constructaprobabilitydistributionforadiscreterandomvariable,determineitsmeanandvariance,andspecifytheprobabilitythatadisc
2、reterandomvariablewillhaveagivenvalueorvalueinagivenrange. 2002 The Wadsworth Group第1页/共19页第一页，共20页。Chapter6-KeyTermsRandomvariablesDiscreteContinuousBernoulliprocessProbabilitydistributionsBinomialdistributionPoissondistribution 2002 The Wadsworth Group第2页/共19页第二页，共20页。DiscretevsContinuousVariables
3、DiscreteVariables:CantakeononlycertainvaluesalonganintervalthenumberofsalesmadeinaweekthevolumeofmilkboughtatastorethenumberofdefectivepartsContinuousVariables:Cantakeonanyvalueatanypointalonganintervalthedepthatwhichadrillingteamstrikesoilthevolumeofmilkproducedbyacowtheproportionofdefectiveparts 2
4、002 The Wadsworth Group第3页/共19页第三页，共20页。DescribingtheDistributionforaDiscreteRandomVariableTheprobabilitydistributionforadiscreterandomvariabledefinestheprobabilityofadiscretevaluex.Mean:=E(x)=Variance:s2=E(x)2= 2002 The Wadsworth Group第4页/共19页第四页，共20页。TheBernoulliProcess,Characteristics1.Therearetw
5、oormoreconsecutivetrials.2.Ineachtrial,therearejusttwopossibleoutcomes.3.Thetrialsarestatisticallyindependent.4.Theprobabilityofsuccessremainsconstanttrial-to-trial. 2002 The Wadsworth Group第5页/共19页第五页，共20页。TheBinomialDistributionThebinomialprobabilitydistributiondefinestheprobabilityofexactlyxsucce
6、ssesinntrialsoftheBernoulliprocess.foreachvalueofx.Mean:=E(x)=npVariance:s2=E(x)2=np(1p) 2002 The Wadsworth Group第6页/共19页第六页，共20页。TheBinomialDistribution,AnExampleWorkedbyEquationProblem6.23:AstudybytheInternationalCoffeeAssociationfoundthat52%oftheU.S.populationaged10andoverdrinkcoffee.Forarandomly
7、selectedgroupof4individuals,whatistheprobabilitythat3ofthemarecoffeedrinkers?NumberProportionCoffeedrinkers(x)3.52Noncoffeedrinkers1.48Totals41.00So,p=0.52,(1p)=0.48,x=3,(nx)=1. 2002 The Wadsworth Group第7页/共19页第七页，共20页。TheBinomialDistribution,WorkingwiththeEquationTosolvetheproblem,wesubstitute: 200
8、2 The Wadsworth Group第8页/共19页第八页，共20页。TheBinomialDistribution,AnExampleWorkedwithTablesProblem:Accordingtoacorporateassociation,50.0%ofthepopulationofVermontwereboatingparticipantsduringthemostrecentyear.Forarandomlyselectedsampleof20Vermontresidents,withx=thenumbersampledwhowereboatingparticipantst
9、hatyear,determine:a.E(x)=np=20x0.50=10b.P(x8)GotoAppendix,TableA.2,n=20.Forp =0.5andk=8,P(x8)=0.2517c.P(x=10)GotoAppendix,TableA.1,n=20.Forp=0.5andk=10,P(x=10)=0.1762 2002 The Wadsworth Group第9页/共19页第九页，共20页。Example:BinomialTablesProblem:Accordingtoacorporateassociation,50.0%ofthepopulationofVermont
10、wereboatingparticipantsduringthemostrecentyear.Forarandomlyselectedsampleof20Vermontresidents,withx=thenumbersampledwhowereboatingparticipantsthatyear,determine:d.P(x=12)GotoAppendix,TableA.1,n=20.Forp=0.5andk=12,P(x=12)=0.1201e.P(7x13)GotoAppendix,TableA.2,n=20.Forp=0.5andk=13,P(x13)=0.9423Forp=0.5
11、andk=6,P(x6)=0.0577P(7x13)=0.94230.0577=0.8846 2002 The Wadsworth Group第10页/共19页第十页，共20页。Example:UsingMicrosoftExcelProblem:Accordingtoacorporateassociation,50.0%ofthepopulationofVermontwereboatingparticipantsduringthemostrecentyear.Forarandomlyselectedsampleof20Vermontresidents,withx=thenumbersampl
12、edwhowereboatingparticipantsthatyear,determine:b.P(x8)InacellonanExcelworksheet,type=BINOMDIST(8,20,0.5,true)andyouwillseetheanswer:0.2517c.P(x=10)InacellonanExcelworksheet,type=BINOMDIST(10,20,0.5,false)andyouwillseetheanswer:=0.1762 2002 The Wadsworth Group第11页/共19页第十一页，共20页。Example:UsingMicrosoft
13、ExcelProblem:Accordingtoacorporateassociation,50.0%ofthepopulationofVermontwereboatingparticipantsduringthemostrecentyear.Forarandomlyselectedsampleof20Vermontresidents,withx=thenumbersampledwhowereboatingparticipantsthatyear,determine:d.P(x=12)InacellonanExcelworksheet,type=BINOMDIST(12,20,0.5,fals
14、e)andyouwillseetheanswer:=0.1201e.P(7x13)InacellonanExcelworksheet,type=BINOMDIST(13,20,0.5,true)-BINOMDIST(6,20,0.5,true)andyouwillseetheanswer:=0.8846 2002 The Wadsworth Group第12页/共19页第十二页，共20页。ThePoissonDistributionThePoissondistributiondefinestheprobabilitythataneventwilloccurexactlyxtimesoverag
15、ivenspanoftime,space,ordistance.wherel=themeannumberofoccurrencesoverthespane=2.71828,aconstantMean=Variance=lExample,Problem6.36:Duringthe12p.m.1p.m.noonhour,arrivalsatacurbsidebankingmachinehavebeenfoundtobePoissondistributedwithameanof1.3personsperminute.Ifx=numberofarrivalsperminute,determine:a.
16、E(x)=l=1.3 2002 The Wadsworth Group第13页/共19页第十三页，共20页。ThePoissonDistribution,WorkingwiththeEquationExample,Problem6.36:Duringthe12p.m.1p.m.noonhour,arrivalsatacurbsidebankingmachinehavebeenfoundtobePoissondistributedwithameanof1.3personsperminute.Ifx=numberofarrivalsperminute,determine:b.c.d.P(x2)=0
17、.8571fromAppendixTableA.4,l=1.3,k=2 2002 The Wadsworth Group第14页/共19页第十四页，共20页。ThePoissonDistribution,UsingMicrosoftExcelExample,Problem6.36:b.P(x=0)InacellinanExcelspreadsheet,type=POISSON(0,1.3,false)andyouwillseetheanswer:=0.2725c.P(x=1)InacellinanExcelspreadsheet,type=POISSON(1,1.3,false)andyouw
18、illseetheanswer:=0.3543d.P(x2)InacellinanExcelspreadsheet,type=POISSON(2,1.3,true)andyouwillseetheanswer:=0.8571 2002 The Wadsworth Group第15页/共19页第十五页，共20页。感谢您的欣赏(xnshng)！第19页/共19页第十九页，共20页。内容(nirng)总结Chapter 6 - Learning Objectives。=POISSON(0,1.3,false)。=POISSON(1,1.3,false)。=POISSON(2,1.3,true)。感谢您的欣赏(xnshng)第二十页，共20页。
