soa真题course6examc

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1、SOA真题Course6ExamCExamC,Fall2005FINALANSINATION**1.Aportfolioofpolicieshasproducedthefollos:100100100200300300300400500600DeterminetheempiricalestimateofH(300).(A)Lessthan0.50(B)Atleast0.50,butlessthan0.75(C)Atleast0.75,butlessthan1.00(D)Atleast1.00,butlessthan1.25(E)Atleast1.25ExamC:Fall

2、2005-2-GOONTONEXTPAGE2.Youaregiven:(i)TheconditionaldistributionofthenumberofclaimsperpolicyholderisPoissoneanλ.(ii)Thevariableλhasagammadistributionetersαandθ.(iii)ForpolicyholdersinYear1,thecredibilityestimateforthenumberofclaimsinYear2is0.15.(iv)ForpolicyholderssperyearinYear1andYear2

3、,thecredibilityestimateforthenumberofclaimsinYear3is0.20.Determineθ.(A)Lessthan0.02(B)Atleast0.02,butlessthan0.03(C)Atleast0.03,butlessthan0.04(D)Atleast0.04,butlessthan0.05(E)Atleast0.05ExamC:Fall2005-3-GOONTONEXTPAGE3.ArandomsampleofclaimshasbeendraaBurrdistributioneterα=1andunknoeters

4、θandγ.Youaregiven:(i)75%oftheclaimamountsinthesampleexceed100.(ii)25%oftheclaimamountsinthesampleexceed500.Estimateθbypercentilematching.(A)Lessthan190(B)Atleast190,butlessthan200(C)Atleast200,butlessthan210(D)Atleast210,butlessthan220(E)Atleast220ExamC:Fall2005-4-GOONTONEXTPAGE4.Youareg

5、iven:(i)f(x)isacubicsplineinef(1).(A)1(B)4(C)6(D)8(E)10ExamC:Fall2005-5-GOONTONEXTPAGE5.Foraportfolioofpolicies,youaregiven:(i)ThereisnodeductibleandthepolicylimitvariesbypolichoodestimateofS(1250)undertheassumptionthatthelossesfolloinetheabsolutedifferencebetC:Fall2005-6-GOONTONEXTPAGE