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1、实用标准Sample Space 样本空间Thesetofallpossibleoutcomesofastatisticalexperimentiscalledthesamplespace.Event事件Aneventisasubsetofasamplespace.certainevent（必然事件）：Thesamplespaceitself,iscertainlyanevent,whichiscalledacertainevent,meansthatitalwaysoccursintheexperiment.impossibleevent（不可能事件）：Theempty
2、set,denotedby,isalsoanevent,calledanimpossibleevent,meansthatitneveroccursintheexperiment.Probabilityofevents（概率）Ifthenumberofsuccessesintrailsisdenotedby,andifthesequenceofrelativefrequenciesobtainedforlargerandlargervalueofapproachesalimit,thenthislimitisdefinedastheprobabilityofsuccessi
3、nasingletrial.“equallylikelytooccur”------probability（古典概率）Ifasamplespaceconsistsofsamplepoints,eachisequallylikelytooccur.Assumethattheeventconsistsofsamplepoints,thentheprobabilitythatAoccursisMutuallyexclusive(互斥事件)Definition2.4.1Eventsarecalledmutuallyexclusive,if.Theorem2.4.1Ifandarem
4、utuallyexclusive,then(2.4.1)Mutuallyindependent事件的独立性TwoeventsandaresaidtobeindependentifOrTwoeventsandareindependentifandonlyif.文档实用标准ConditionalProbability条件概率Theprobabilityofaneventisfrequentlyinfluencedbyotherevents.DefinitionTheconditionalprobabilityof,given,denotedby,isdefinedbyif.(2
5、.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.）Theorem2.6.2Iftheeventsconstituteapartitionofthesamplespa
6、ceSsuchthatforthanforanyeventAofS,,.for(2.6.2)ProofBythedefinitionofconditionalprobability,文档实用标准Usingthetheoremoftotalprobability,wehave1.randomvariabledefinitionDefinition3.1.1Arandomvariableisarealvaluedfunctiondefinedonasamplespace;i.e.itassignsarealnumbertoeachsamplepointinthesamplesp
7、ace.2.DistributionfunctionDefinition3.1.2Letbearandomvariableonthesamplespace.Thenthefunction.iscalledthedistributionfunctionofNoteThedistributionfunctionisdefinedonrealnumbers,notonsamplespace.3.PropertiesThedistributionfunctionofarandomvariablehasthefollowin
