统计学英文版教材课件.pdf

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1、STAT7055LECTURE2ProbabilityFebruary17,2016STAT7055-Lecture2February17,20161/64IntroductionDenitionsRandomExperimentIArandomexperimentisaprocessthatresultsinoneofseveralpossibleoutcomes,noneofwhichcanbepredictedwithcertainty.IForexample:IRollingaconventionaldie.Possibleoutcomesare1,2,3,4,5or6.

2、IFlippingacoin.Possibleoutcomesareheadsortails.IOutcomesaredenotedbyOi.STAT7055-Lecture2February17,20162/64IntroductionDenitionsSampleSpaceIThesamplespaceofarandomexperimentisalistofallthepossibleoutcomesandisdenotedbyS=fO1;O2;O3;:::g.IForexample,when ippingacoin,S=fH;Tg.ITheoutcomesinasample

3、spacemustbebothmutuallyexclusiveandexhaustive.IMutuallyexclusive:Notwooutcomescanbothoccuratthesametimeonanysingletrialoftheexperiment.IExhaustive:Thesamplespacemustincludeallpossibleoutcomesthatcanoccur.STAT7055-Lecture2February17,20163/64IntroductionDenitionsProbabilitiesofOutcomesITheproba

4、bilityofanoutcomeoccurringonasingletrialiswrittenasP(Oi).IProbabilitiesassociatedwiththeoutcomesinasamplespacemustsatisfytwoimportantrequirements:1.X0P(Oi)1foralli.2.P(Oi)=1alliSTAT7055-Lecture2February17,20164/64IntroductionThreeApproachesforAssigningProbabilitiesClassicalApproachITheclassi

5、calapproachisbasedontheassumptionthattheoutcomesofanexperimentareequallylikelytohappen.ISupposewerollafairsix-sideddie.IWhatistheprobabilityofrollinga5?IThesamplespaceisS=f1;2;3;4;5;6g.IAssumingallsixoutcomesareequallylikely,theprobabilityofrollinga5isP(5)=1.6INotethatinmorecomplicatedexperime

6、nts,weoftenneedtousemathematicalrulestocountthetotalnumberofoutcomes.STAT7055-Lecture2February17,20165/64IntroductionThreeApproachesforAssigningProbabilitiesRelativeFrequencyApproachITherelativefrequencyapproachdenesprobabilityasthelong-runrelativefrequencywithwhichanoutcomesoccurs.ISupposewe

7、rollaloadedsix-sideddie.IWhatistheprobabilityofrollinga5?IWecan'tassumeequallylikelyoutcomes.IButsupposeweknowthatinthepast1000rolls,a5cameup190times.IBasedonthispasthistory,weassigntheprobabilityofrollinga5tobethelong-runrelativefreque