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- STA642 Probability Distributions
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- 23 Oct 2026
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Quiz1 Theoreticallytherecanbeaninfinitenumberofdecimalplacesafterthedecimals. Page62 Quiz2. CoefficientsofCorrelationareindependentofChangeofOrigin: ThispropertyrevealsthatifwesubtractanyconstantfromallthevaluesofX(oraddany constanttoallthevaluesofX)Page865 .CoefficientofCorrelationisindependentofChangeofScale: ThispropertyrevealsthatifwedivideormultiplyallthevaluesofXbyanyconstantanddivide ormultiplyallthevaluesofYbyanyconstant,itwillnotaffectthecoefficientofcorrelation
Quiz3Jacobian(denotedbyJ)ofthetransformation. Page254 Quiz4say,20%isknownasthe20thpercentile,thepointtotheleftofwhichtheareais,say, 35%isknownasthe35thpercentileandsoPage296 Quiz5•ThequantilefunctionisalsocalledtheinversecumulativedistributionfunctionPage
Quiz6Thejointprobabilitydistributioncanbeexpressedeitherintermsofajointcumulative distributionfunctionorintermsofajointprobabilitydensityfunction(inthecaseofcontinuous variables)orjointprobabilitymassfunction(inthecaseofdiscretevariables).Page583 Quiz7(CumulativeDistributionFunction)thediscretecaseitislikeastaircasePage114 Quiz8CoefficientofCorrelationisindependentofChangeofScale: Quiz9LetXbearandomvector. ThentheexpectedvalueofXexistsiftheexpectationsofX1 andX2exist. Page738 Quiz10ThecentralmomentgeneratingfunctionisgivendenotedbyC(t)Page515
Quiz11correlation
Quiz126. IftwovariablesXandYareindependent,coefficientofcorrelationbetweenthemwill bezero. Page873 Quiz13Anyexperimentorprocessinwhichtheoutcomeisunpredictablethatiseligibletobe calledarandomPage3 Quiz14Foranydistribution,ifahighermomentexists,thenalllowermomentsnecessarily exists. Page815 Quiz15TheconditionalprobabilityofevenA,giveneventB,as Page819ThisnumberiscalledthecovarianceofXandYand
isoftendenotedbycov(X, Y).Page849 Quiz16Ifxandyaretworealnumbersthantheabsolutevalue(themodulus)of|x+y|isless thanorequaltothemodulusof|x|andmodulusof|y|
Quiz17LetXbearandomvariablewithcumulativedistributionfunctionF(x). Then,(b)limx→ -∞,F(x)=0(thelowerlimitofFis0).Page152 Quiz18cdfthejointcumulativedistributionfunctionPage587 Quiz19Maclaurin’sseriesPage447 Quiz20probabilitydensityfunction(pdf)Page64 Quiz21 arandomvariablefitisfinite,thentheexpectationexistsandwecandetermineits expectationbyobtainingthedistributionandifitisinfinite(i.e.ifitisnotfinite),weshallsay thattheexpectationofXdoesnotexistPage6882Quiz Quiz22jointprobabilitydistributionInthecaseofonlytworandomvariables,thisiscalleda bivariatedistributionPage582 Quiz23ForacontinuousrandomvariableX,theCDFisasfollows: •F(x)=0forallxvalueswhicharelessthanzero •F(x)=xforallthosexvaluesthatliesbetween0and1. •F(x)=1forallthosexvaluesaregreaterthan1. Page130
Quiz24
Thisissometimescalledthelawoftotalexpectationandsometimesitiscalledthelawof iteratedexpectations. Page844 Quiz25SampleSpaceItisthesetofallpossibleoutcomesofarandomexperimentPage8 Quiz26probabilitydensityfunctionf(x)Page692 Quiz27TheconceptoftheCDF,willalwaysbemonotonicallyincreasingfunction. Page194
Quiz28TheCharacteristicfunction Page7942quiz
Quiz29P(X=x)=1/6fairdie1,2, 3, 4, 5, 6Page43 Quiz30cumulativedistributionfunctionF(x).Page57 Quiz31 •Inthecontinuouscase,themarginalpdfofX1isfoundbyintegratingoutx2,
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