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.精选范本SampleSpace样本空间Thesetofallpossibleoutcomesofastatisticalexperimentiscalledthesamplespace.Event事件Aneventisasubsetofasamplespace.certainevent（必然事件）：Thesamplespaceitself,iscertainlyanevent,whichiscalledacertainevent,meansthatitalwaysoccursintheexperiment.impossibleevent（不可能事件）：Theemptyset,denotedby,isalsoanevent,calledanimpossibleevent,meansthatitneveroccursintheexperiment.Probabilityofevents（概率）Ifthenumberofsuccessesintrailsisdenotedby,andifthesequenceofrelativefrequenciesobtainedforlargerandlargervalueofapproachesalimit,thenthislimitisdefinedastheprobabilityofsuccessinasingletrial.“equallylikelytooccur”------probability（古典概率）Ifasamplespaceconsistsofsamplepoints,eachisequallylikelytooccur.Assumethattheeventconsistsofsamplepoints,thentheprobabilitythatAoccursisMutuallyexclusive(互斥事件)Definition2.4.1Eventsarecalledmutuallyexclusive,if.Theorem2.4.1Ifandaremutuallyexclusive,then(2.4.1)Mutuallyindependent事件的独立性TwoeventsandaresaidtobeindependentifOrTwoeventsandareindependentifandonlyif.ConditionalProbability条件概率Theprobabilityofaneventisfrequentlyinfluencedbyotherevents.DefinitionTheconditionalprobabilityof,given,denotedby,isdefinedbyif.(2.5.1)Themultiplicationtheorem乘法定理Ifareevents,thenIftheeventsareindependent,thenforanysubset,(全概率公式totalprobability)Theorem2.6.1.IftheeventsconstituteapartitionofthesamplespaceSsuchthatforthanforanyeventof,(2.6.2)（贝叶斯公式Bayes’formula.）Theorem2.6.2IftheeventsconstituteapartitionofthesamplespaceSsuchthatforthanforanyeventAofS,,.for(2.6.2)ProofBythedefinitionofconditionalprobability,Usingthetheoremoftotalprobability,wehave1.randomvariabledefinitionDefinition3.1.1Arandomvariableisarealvaluedfunctiondefinedonasamplespace;i.e.itassignsarealnumbertoeachsamplepointinthesamplespace.2.DistributionfunctionDefinition3.1.2Letbearandomvariableonthesamplespace.Thenthefunction.iscalledthedistributionfunctionofNoteThedistributionfunctionisdefinedonrealnumbers,notonsamplespace.3.PropertiesThedistribut
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