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,butlesstha

2、n1.25(E)Atleast1.25ExamC:Fall2005-2-GOONTONEXTPAGE2.Youaregiven:(i)TheconditionaldistributionofthenumberofclaimsperpolicyholderisPoissoneanλ.(ii)Thevariableλhasagammadistributionetersαandθ.(iii)ForpolicyholdersinYear1,thecredibilityestimateforthenumberofclaim

3、sinYear2is0.15.(iv)ForpolicyholderssperyearinYear1andYear2,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

4、-3-GOONTONEXTPAGE3.ArandomsampleofclaimshasbeendraaBurrdistributioneterα=1andunknoetersθandγ.Youaregiven:(i)75%oftheclaimamountsinthesampleexceed100.(ii)25%oftheclaimamountsinthesampleexceed500.Estimateθbypercentilematching.(A)Lessthan190(B)Atleast190,butless

5、than200(C)Atleast200,butlessthan210(D)Atleast210,butlessthan220(E)Atleast220ExamC:Fall2005-4-GOONTONEXTPAGE4.Youaregiven:(i)f(x)isacubicsplineinef(1).(A)1(B)4(C)6(D)8(E)10ExamC:Fall2005-5-GOONTONEXTPAGE5.Foraportfolioofpolicies,youaregiven:(i)Thereisnodeducti

6、bleandthepolicylimitvariesbypolichoodestimateofS(1250)undertheassumptionthatthelossesfolloinetheabsolutedifferencebetC:Fall2005-6-GOONTONEXTPAGE