spring 2003 exam

《spring 2003 exam》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、1.Asurveyofagroup’sviewinghabitsoverthelastyearrevealedthefollowinginformation:(i)28%watchedgymnastics(ii)29%watchedbaseball(iii)19%watchedsoccer(iv)14%watchedgymnasticsandbaseball(v)12%watchedbaseballandsoccer(vi)10%watchedgymnasticsandsoccer(vii)8%wa

2、tchedallthreesports.Calculatethepercentageofthegroupthatwatchednoneofthethreesportsduringthelastyear.(A)24(B)36(C)41(D)52(E)60Course16Form03A2.Eachofthegraphsbelowcontainstwocurves.Identifythegraphcontainingacurverepresentingafunctionyfx=()andacurverep

3、resentingitssecondderivativeyfx=′′().(A)(B)(C)(D)(E)May20037Course13.Letfandgbedifferentiablefunctionssuchthatlimf(xc)=x→0limgxd()=x→0wherecd≠.Determinelimcfx()−dgx().x→0f()xgx−()(A)0cf′′()00−dg()(B)fg′′()00−()(C)fg′′()00−()(D)cd−(E)cd+Course18Form03A4

4、.Thetimetofailureofacomponentinanelectronicdevicehasanexponentialdistributionwithamedianoffourhours.Calculatetheprobabilitythatthecomponentwillworkwithoutfailingforatleastfivehours.(A)0.07(B)0.29(C)0.38(D)0.42(E)0.57May20039Course15.Aninsurancecompanye

5、xaminesitspoolofautoinsurancecustomersandgathersthefollowinginformation:(i)Allcustomersinsureatleastonecar.(ii)70%ofthecustomersinsuremorethanonecar.(iii)20%ofthecustomersinsureasportscar.(iv)Ofthosecustomerswhoinsuremorethanonecar,15%insureasportscar.

6、Calculatetheprobabilitythatarandomlyselectedcustomerinsuresexactlyonecarandthatcarisnotasportscar.(A)0.13(B)0.21(C)0.24(D)0.25(E)0.30Course110Form03A6.LetXandYbecontinuousrandomvariableswithjointdensityfunction8xyxfor0≤≤≤≤1,xy2xfxy(,)=30otherwise.

7、CalculatethecovarianceofXandY.(A)0.04(B)0.25(C)0.67(D)0.80(E)1.24May200311Course1247.Given∫∫fxdx()==3andfxdx()5,022calculate∫f()2xdx.0(A)32(B)3(C)4(D)6(E)8Course112Form03A8.Anautoinsurancecompanyinsuresdriversofallages.Anactuarycompiledthefollowingstat

8、isticsonthecompany’sinsureddrivers:AgeofProbabilityPortionofCompany’sDriverofAccidentInsuredDrivers16-200.060.0821-300.030.1531-650.020.4966-990.040.28Arandomlyselecteddriverthatthecompanyinsureshasanaccident.Calculatetheprobabilitythat