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1、Chapter2StatisticReviewA.Randomvariables;1.expectedvalue:Define:Xisadiscreterandomvariable,“themean(orexpectedvalue)ofX”istheweightedaverageofthepossibleoutcomes,wheretheprobabilitiesoftheoutcomeserveastheappropriateweight.piisithofprob.,i=1,2,……nInterpretation
2、:Therandomvariableisavariablethathaveaprobabilityassociatedwitheachoutcome.Outcomeisnotcontrolled.DiscreterandomVar.:hasfiniteoutcome,oroutcomeiscountableinfinite.ContinuousrandomVar.:uncountableinfiniteoutcome,theprobabilityofeachoutcomeissmallbecauseoftoomany
3、numbers.FornormalrandomVar.,probabilitydensityfunctionisusedtocalculatetheprobabilitybetweentheare.E():theexpectationsoperator,à…“samplemean”,usedtoestimateTheischangedfromsampletosample.isnotafixedontime,theoutcomeselectedshouldnotbethesame.Thereisprob.associa
4、tedwitheach.isalsoarandomvariable,wecancalculateE().2.variance:measurethedispersion(分散),therangeofthevalue“populationvariance”constant…………...“populationstandarddeviation”à“samplevariance”usedtoestimate………..“samplestandarddeviation”153.jointdistribution:(linearr
5、elationofXandYbi-variancerandomvariance.)Covariance,measuringthelinearrelationshipbetweenXandY.,dependsontheunitsofXandY;differentunit->different>0:thebest-fittinglinehasapositiveslope,positiverelationshipbetweenXandY.<0:thebest-fittinglinehasanegativeslope,neg
6、ativerelationshipbetweenXandY.=0:thereisnolinearrelationshipbetweenXandY,butmaybehavenonlinearrelationship.“populationcorrelationcoefficient”isscalefree.>0,apositivecorrection,<0,anegativecorrection=0,nolinearrelationshipbetweenXandY,=1:regressionlineisastraigh
7、tlinewithpositiveslope,=-1:regressionlineisastraightlinewithnegativeslope.,=“samplecorrelationcoefficient”15Ex：jointprob.distributionofXandYX123Prob(Y)Y60.1750.0880.0350.29850.0700.2100.1050.38540.0180.1050.1940.317Prob(X)0.2630.4030.3341E(X)=0.263×1+0.403×2+0.
8、334×3=2.071Var(X)=4.881-(2.071)2=0.591959E(Y)=0.298×6+0.385×5+0317×4=4.981Var(Y)=25.425-(4.981)2=0.614639Cov(X,Y)==10.001-2.071×4.981=-0.3174.formulaE(b)=b,Var(b)=0；E(aX)=aE
