实用文案标准Class1:Expectations,variances,andbasicsofestimationBasicsofmatrix(1)I.OrganizationalMatters(1)Courserequirements:1)Exercises:Therewillbeseven(7)exercises,thelastofwhichisoptional.Eachexercisewillbegradedonascaleof0-10.Inadditiontothegradedexercise,ananswerhandoutwillbegiventoyouinlabsections.2)Examination:Therewillbeonein-class,open-bookexamination.(2)Computersoftware:StataII.TeachingStrategies(1)Emphasisonconceptualunderstanding.Yes,wewilldealwithmathematicalformulas,actuallyalotofmathematicalformulas.But,Idonotwantyoutomemorizethem.WhatIhopeyouwilldo,istounderstandthelogicbehindthemathematicalformulas.(2)Emphasisonhands-onresearchexperience.Yes,wewillusecomputersformostofourwork.ButIdonotwantyoutobecomeacomputerprogrammer.Manypeoplethinktheyknowstatisticsoncetheyknowhowtorunastatisticalpackage.Thisiswrong.Doingstatisticsismorethanrunningcomputerprograms.WhatIwillemphasizeistousecomputerprogramstoyouradvantageinresearchsettings.Computerprogramsarelikeautomobiles.Thebestautomobileisuselessunlesssomeonedrivesit.Youwillbethedriverofstatisticalcomputerprograms.(3)Emphasisonstudent-instructorcommunication.Ihappentobelieveinstudents'judgmentabouttheirowneducation.EventhoughIwillbeultimatelyresponsibleiftheclassshouldnotgowell,Ihopethatyouwillfeelpartoftheclassandcontributetothequalityofthecourse.Ifyouhavequestions,donothesitatetoaskinclass.Ifyouhavesuggestions,pleasecomeforwardwiththem.Theclassisasmuchyoursasmine.Nowletusgettotherealbusiness.III(1).ExpectationandVarianceRandomVariable:Arandomvariableisavariablewhosenumericalvalueisdeterminedbytheoutcomeofarandomtrial.Twoproperties:randomandvariable.Arandomvariableassignsnumericvaluestouncertainoutcomes.Inacommonlanguage,"giveanumber".Forexample,incomecanbearandomvariable.Therearemanywaystodoit.Youcanusetheactualdollaramounts.Inthiscase,youhaveacontinuousrandomvariable.Oryoucanuselevelsofincome,suchashigh,median,andlow.Inthiscase,youhaveanordinalrandomvariable[1=high,Class1,Page22=median,3=low].Orifyouareinterestedintheissueofpoverty,youcanhaveadichotomousvariable:1=inpoverty,0=notinpoverty.Insum,themappingofnumericvaluestooutcomesofeventsinthiswayistheessenceofarandomvariable.ProbabilityDistribution:TheprobabilitydistributionforadiscreterandomvariableXassociateswitheachofthedistinctoutcomesxi(i=1,2,...,k)aprobabilityP(X=xi).CumulativeProbabilityDistribution:ThecumulativeprobabilitydistributionforadiscreterandomvariableXprovidesthecumulativeprobabilitiesP(Xx)forallvaluesx.ExpectedValueofRandomVariable:TheexpectedvalueofadiscreterandomvariableXisdenotedbyE{X}anddefined:E{X}=P(xi)where:P(xi)denotesP(X=xi).ThenotationE{}(read“expectationof”)iscalledtheexpectationoperator.Incommonlanguage,expectationisthemean.Butthedifferenceisthatexpectationisaconceptfortheentirepopulationthatyouneverobserve.Itistheresultoftheinfinitenumberofrepetitions.Forexample,ifyoutossacoin,theproportionoftailsshouldbe.5inthelimit.Ortheexpectationis.5.Mostofthetimesyoudonotgettheexact.5,butanumberclosetoit.ConditionalExpectationItisthemeanofavariableconditionalonthevalueofanotherrandomvariable.Notethenotation:E(Y|X).In1996,per-capitaaveragewagesinthreeChinesecitieswere(inRMB):Shanghai:3,778Wuhan:1,709Xi’an:1,155VarianceofRandomVariable:ThevarianceofadiscreterandomvariableXisdenotedbyV{X}anddefined:V{X}=(xi-E{X})2P(xi)where:P(xi)denotesP(X=xi)...
