spring 2001 exam

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1、COURSE1MAY2001–bn1.Thepriceofaninvestmentattheendofmonthnismodeledbypn=newherebisaconstant.Themodelpredictsthatthepriceattheendofthesixthmonthisthesameasthepriceattheendofthefifthmonth.Determineb.5(A)ln655(B)ln6656(C)ln657(D)ln66(E)ln5May

2、20017Course12.Astockpaysannualdividends.Thefirstdividendis8andeachdividendthereafteris7%largerthanthepriordividend.Letmbethenumberofdividendspaidbythestockwhenthecumulativeamountpaidfirstexceeds500.Calculatem.(A)23(B)24(C)25(D)26(E)27May20018Course123.Thecoordinatesof

3、anobjectmovinginRare:tx=4sin2y=2tcostfortimet>0.πCalculatethelengthofthevelocityvectoroftheobjectattimet=.2(A)2(B)π2(C)π+22(D)π+4(E)π+2May20019Course14.Acompanyagreestoacceptthehighestoffoursealedbidsonaproperty.Thefourbidsareregardedasfourindependentrandomvariableswi

4、thcommoncumulativedistributionfunction135Fx()=+()1sinπxfor≤≤x.222Whichofthefollowingrepresentstheexpectedvalueoftheacceptedbid?5/2(A)ππ∫xxcosdx3/25/214(B)∫()1sin+πxdx163/25/214(C)∫xx()1sin+πdx163/25/213(D)ππ∫cosxx()1sin+πdx43/25/213(E)πππ∫xxcos()1sin+xdx43/2May200110C

5、ourse15.Acompanyisreviewingtornadodamageclaimsunderafarminsurancepolicy.LetXbetheportionofaclaimrepresentingdamagetothehouseandletYbetheportionofthesameclaimrepresentingdamagetotherestoftheproperty.ThejointdensityfunctionofXandYis61([]−+xy)forx>0,y>0,xy+<1fxy(,)=

6、0otherwise.Determinetheprobabilitythattheportionofaclaimrepresentingdamagetothehouseislessthan0.2.(A)0.360(B)0.480(C)0.488(D)0.512(E)0.520May200111Course16.Aninsurancecompanyissueslifeinsurancepoliciesinthreeseparatecategories:standard,preferred,andultra-preferred.Oft

7、hecompany’spolicyholders,50%arestandard,40%arepreferred,and10%areultra-preferred.Eachstandardpolicyholderhasprobability0.010ofdyinginthenextyear,eachpreferredpolicyholderhasprobability0.005ofdyinginthenextyear,andeachultra-preferredpolicyholderhasprobability0.001ofdyi

8、nginthenextyear.Apolicyholderdiesinthenextyear.Whatistheprobabilitythatthedeceasedpolicyholderwasultra-preferred?(A)0.0001(B