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1、Randomsampling(随机抽样)Independent（独立性）Representative（代表性）ThepoliticalsystemoftheUSTheUSSenate(参议院）EachstateallowstwosenatorsSothereareabout100senatorsin50states.TheHouseofrepresentatives（众议院）Thenumberofrepresentativesfromeachstatedependsonitspopulation
2、California56NewYork33Texas32Delaware3Tennessee12Florida25Usingrandomnumberstoimplementrandomsampling128934567…100…SamplingprobabilitySussexUniversityhas1000students.200ofthemareforeignstudents,othersareAmerican.Whatistheprobabilityofrandomlysamplinga
3、foreignstudentinonetrial?ThesamplingsizeIfyouselect1studentfrom1000,thentheoutcomeofprobabilitywouldbeeither0%or100%.Ifyouselectmany,thentheoutcomewouldapproach20%Thecoin-tossexperimentExperimenterTimesoftoss,nHeaduptimes,mFrequency,m/nBuffon40402048
4、0.5069Pearson1200060190.5016Pearson24000120120.5005Head/TailThelawoflargenumbers(大数定律)Whensamplingsizeissufficientlylarge,thesamplingmeanoutcomecalculatedfromrepeatedobservationsofarandomvariablemustapproachthedistributionprobability.limP{f/n–p<ε}=1n
5、∞f:frequencyoftheeventsp:theoreticalprobabilityn:samplingsizeε:aninfinitesimalnumberThelawoflargenumbersThelawoflargenumbersisthefoundationuponwhichsuchbusinessenterprisesasgamblingcasinosandinsurancecompaniesarebuiltSamplingprobabilitySussexUnivers
6、ityhas1000students.200ofthemareforeignstudents,othersareAmerican.Whatistheprobabilityofgetting2foreignstudentintwosamples?FFAAAFFASamplingpoint(样本点）Samplingspace（样本空间）{FF,FA,AA}{p2,2pq,q2}p=P[F]=200/1000q=P[A]=800/1000p+q=1Theprobabilityofindependent
7、lysampling2students{FFF,FFA,FAA,AAA}{p3,3p2q,3pq2,q3}Theprobabilityofindependentlysampling3studentsGivenp=0.2,q=0.8,thentheprobabilityvalues:{0.008,0.096,0.384,0.512}0123ProbabilitydistributionForsamplesof1,p+qForsamplesof2,(p+q)2=p2+2pq+q2Forsamples
8、of3,(p+q)3=p3+3p2q+3pq2+q3…Forsamplesofn,(p+q)n=ThecoefficientsoftheexpandedtermsPascal’striangle:1112113311464115101051n12345…Forsamplesof4,(p+q)4=p4+4p3q+6p2q2+4pq3+q4Thebinomialdistribution(二项分布)Pn(k)=Cnkpkqn-kX012…k…nPqnnpqn-1Cn2p2qn-2…Cnkpkqn-k…
