商务统计全套配套课件[美]AmirD.AczelJayavelSounderpandian著谭英平等译Chap003.ppt

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1、COMPLETEBUSINESSSTATISTICSbyAMIRD.ACZEL&JAYAVELSOUNDERPANDIAN6thedition.Chapter3RandomVariablesUsingStatisticsExpectedValuesofDiscreteRandomVariablesSumandLinearCompositeofRandomVariablesBernoulliRandomVariableTheBinomialRandomVariableTheGeometricDistributionTheHypergeometricDistributionThePoisson

2、DistributionContinuousRandomVariablesUniformDistributionTheExponentialDistributionRandomVariables3Afterstudyingthischapteryoushouldbeableto:DistinguishbetweendiscreteandcontinuousrandomvariablesExplainhowarandomvariableischaracterizedbyitsprobabilitydistributionComputestatisticsaboutarandomvariableC

3、omputestatisticsaboutafunctionofarandomvariableComputestatisticsaboutthesumoralinearcompositeofarandomvariableIdentifywhichtypeofdistributionagivenrandomvariableismostlikelytofollowSolveproblemsinvolvingstandarddistributionsmanuallyusingformulasSolvebusinessproblemsinvolvingstandarddistributionsusin

4、gspreadsheettemplates.LEARNINGOBJECTIVES3Considerthedifferentpossibleorderingsofboy(B)andgirl(G)infoursequentialbirths.Thereare2*2*2*2=24=16possibilities,sothesamplespaceis:BBBBBGBBGBBBGGBBBBBGBGBGGBBGGGBGBBGBBGGBGBGBGGGBBBGGBGGGGBGGGGGGIfgirlandboyareeachequallylikely[P(G)=P(B)=1/2],andthegenderofe

5、achchildisindependentofthatofthepreviouschild,thentheprobabilityofeachofthese16possibilitiesis:(1/2)(1/2)(1/2)(1/2)=1/16.3-1UsingStatisticsNowcountthenumberofgirlsineachsetoffoursequentialbirths:BBBB(0)BGBB(1)GBBB(1)GGBB(2)BBBG(1)BGBG(2)GBBG(2)GGBG(3)BBGB(1)BGGB(2)GBGB(2)GGGB(3)BBGG(2)BGGG(3)GBGG(3)

6、GGGG(4)Noticethat:eachpossibleoutcomeisassignedasinglenumericvalue,alloutcomesareassignedanumericvalue,andthevalueassignedvariesovertheoutcomes.Thecountofthenumberofgirlsisarandomvariable:Arandomvariable,X,isafunctionthatassignsasingle,butvariable,valuetoeachelementofasamplespace.RandomVariablesRand

7、omVariables(Continued)BBBBBGBBGBBBBBBGBBGBGGBBGBBGBGBGBGGBGBGBBBGGBGGGGBGGGGGBGGBGGGGG01234XSampleSpacePointsontheRealLineSincetherandomvariableX=3whenanyofthefouroutcomesBGGG,GBGG,GGBG,orGGGBoccurs,P