CFA特許金融分析師-CFA一級-01-QuantitativeMethods

CFA特許金融分析師-CFA一級-01-QuantitativeMethods[單選題]1.XisadiscreterandomvariablewithpossibleoutcomesX=（江南博哥）{1,2,3,4}.Threefunctionsf(x),g(x),andh(x)areproposedtodescribetheprobabilitiesoftheoutcomesinX.

Theconditionsforaprobabilityfunctionaresatisfiedby:A.f(x).B.g(x).C.h(x).正確答案：B參考解析：Biscorrect.Thefunctiong(x)satisfiestheconditionsofaprobabilityfunction.Allofthevaluesofg(x)arebetween0and1,andthevaluesofg(x)allsumto1.[單選題]2.AMonteCarlosimulationcanbeusedto:A.directlyprovideprecisevaluationsofcalloptions.B.simulateaprocessfromhistoricalrecordsofreturns.C.testthesensitivityofamodeltochangesinassumptions.正確答案：C參考解析：Ciscorrect.AcharacteristicfeatureofMonteCarlosimulationisthegenerationofalargenumberofrandomsamplesfromaspecifiedprobabilitydistributionordistributionstorepresenttheroleofriskinthesystem.[單選題]3.ThefollowingisafrequencypolygonofmonthlyexchangeratechangesintheUSdollar/Japaneseyenspotexchangerateforafour-yearperiod.Apositivechangerepresentsyenappreciation(theyenbuysmoredollars),andanegativechangerepresentsyendepreciation(theyenbuysfewerdollars).

Basedonthechart,yenappreciation:A.occurredmorethan50%ofthetime.B.waslessfrequentthanyendepreciation.C.inthe0.0to2.0intervaloccurred20%ofthetime.正確答案：A參考解析：Aiscorrect.Twentyobservationslieintheinterval“0.0to2.0,”andsixobservationslieinthe2.0to4.0interval.Together,theyrepresent26/48,or54.17%ofallobservations,whichismorethan50%.[單選題]4.Adistributionwithexcesskurtosislessthanzeroistermed:A.mesokurtic.B.platykurtic.C.leptokurtic.正確答案：B參考解析：Biscorrect.Aplatykurticdistributionhasexcesskurtosislessthanzero.Aisincorrectbecauseanormalorothermesokurticdistributionhasexcesskurtosisequaltozero.Cisincorrectbecausealeptokurticdistributionhasexcesskurtosisgreaterthanzero.[單選題]5.Whichparameterequalszeroinanormaldistribution?A.KurtosisB.SkewnessC.Standarddeviation正確答案：B參考解析：Biscorrect.Anormaldistributionhasaskewnessofzero(itissymmetricalaroundthemean).Anon-zeroskewnessimpliesasymmetryinadistribution.[單選題]6.Johnpurchased60%ofthestocksinaportfolio,whileAndrewpurchasedtheother40%.HalfofJohn’sstock-picksareconsideredgood,whileafourthofAndrew’sareconsideredtobegood.Ifarandomlychosenstockisagoodone,whatistheprobabilityJohnselectedit?A.0.40.B.0.30.C.0.75.正確答案：C參考解析：Usingtheinformationofthestockbeinggood,theprobabilityisupdatedtoaconditionalprobability:P(John|good)=P(goodandJohn)/P(good).P(goodandJohn)=P(good|John)×P(John)=0.5×0.6=0.3.P(goodandAndrew)=0.25×0.40=0.10.P(good)=P(goodandJohn)+P(goodandAndrew)=0.40.P(John|good)=P(goodandJohn)/P(good)=0.3/0.4=0.75.[單選題]7.Indescriptivestatistics,anexampleofaparameteristhe:A.medianofapopulation.B.meanofasampleofobservations.C.standarddeviationofasampleofobservations.正確答案：A參考解析：Aiscorrect.Anydescriptivemeasureofapopulationcharacteristicisreferredtoasaparameter.[單選題]8.Asportscar,purchasedfor￡200,000,isfinancedforfiveyearsatanannualrateof6%compoundedmonthly.Ifthefirstpaymentisdueinonemonth,themonthlypaymentisclosestto:A.￡3,847.B.￡3,867.C.￡3,957.正確答案：B參考解析：Biscorrect,calculatedasfollows(whereAisannuityandPVispresentvalue):[單選題]9.Aperpetualpreferredstockmakesitsfirstquarterlydividendpaymentof$2.00infivequarters.Iftherequiredannualrateofreturnis6%compoundedquarterly,thestock’spresentvalueisclosestto:A.$31.B.$126.C.$133.正確答案：B參考解析：Biscorrect.Thevalueoftheperpetuityoneyearfromnowiscalculatedas:PV=A/r,wherePVispresentvalue,Aisannuity,andrisexpressedasaquarterlyrequiredrateofreturnbecausethepaymentsarequarterly.[單選題]10.Theheightofabarinahistogramrepresentsthematchingdatainterval’s:A.relativefrequency.B.absolutefrequency.C.cumulativefrequency.正確答案：B參考解析：Biscorrect.Inahistogram,theheightofeachbarrepresentstheabsolutefrequencyofitsassociateddatainterval.Aisincorrectbecausetheheightofeachbarinahistogramrepresentstheabsolute(notrelative)frequency.Cisincorrectbecausetheheightofeachbarinahistogramrepresentstheabsolute(notcumulative)frequency.[單選題]11.Iftheprobabilitythataportfoliooutperformsitsbenchmarkinanyquarteris0.75,theprobabilitythattheportfoliooutperformsitsbenchmarkinthreeorfewerquartersoverthecourseofayearisclosestto:A.0.26B.0.42C.0.68正確答案：C參考解析：Ciscorrect.TheprobabilitythattheperformanceisatorbelowtheexpectationiscalculatedbyfindingF(3)=p(3)+p(2)+p(1)usingtheformula:

Therefore,F(3)=p(3)+p(2)+p(1)+p(0)=0.42+0.20+0.06+0.004=0.684orapproximately68percent[單選題]12.Whichofthefollowingstatementsiscorrectwithrespecttothep-value?A.Itisalessprecisemeasureoftestevidencethanrejectionpoints.B.Itisthelargestlevelofsignificanceatwhichthenullhypothesisisrejected.C.Itcanbecompareddirectlywiththelevelofsignificanceinreachingtestconclusions.正確答案：C參考解析：Ciscorrect.Whendirectlycomparingthep-valuewiththelevelofsignificance,itcanbeusedasanalternativetousingrejectionpointstoreachconclusionsonhypothesistests.Ifthep-valueissmallerthanthespecifiedlevelofsignificance,thenullhypothesisisrejected.Otherwise,thenullhypothesisisnotrejected.[單選題]13.Whichofthefollowingischaracteristicofthenormaldistribution?A.AsymmetryB.Kurtosisof3C.Definitivelimitsorboundaries正確答案：B參考解析：Biscorrect.Thenormaldistributionhasaskewnessof0,akurtosisof3,andamean,medianandmodethatareallequal.[單選題]14.Givena€1,000,000investmentforfouryearswithastatedannualrateof3%compoundedcontinuously,thedifferenceinitsinterestearningscomparedwiththesameinvestmentcompoundeddailyisclosestto:A.€1.B.€6.C.€455.正確答案：B參考解析：Biscorrect.Thedifferencebetweencontinuouscompoundinganddailycompoundingis€127,496.85–€127,491.29=€5.56,or≈€6,asshowninthefollowingcalculations.Withcontinuouscompounding,theinvestmentearns(wherePVispresentvalue)

Withdailycompounding,theinvestmentearns:[單選題]15.ATypeIIerrorisbestdescribedas:A.rejectingatruenullhypothesis.B.failingtorejectafalsenullhypothesis.C.failingtorejectafalsealternativehypothesis.正確答案：B參考解析：Biscorrect.ATypeIIerroroccurswhenafalsenullhypothesisisnotrejected.[單選題]16.AlimitationofMonteCarlosimulationis:A.itsfailuretodo“whatif”analysis.B.thatitrequireshistoricalrecordsofreturnsC.itsinabilitytoindependentlyspecifycause-and-effectrelationships.正確答案：C參考解析：Ciscorrect.MonteCarlosimulationisacomplementtoanalyticalmethods.MonteCarlosimulationprovidesstatisticalestimatesandnotexactresults.Analyticalmethods,whenavailable,providemoreinsightintocause-and-effectrelationships[單選題]17.Aninvestmentof€500,000todaythatgrowsto€800,000aftersixyearshasastatedannualinterestrateclosestto:A.7.5%compoundedcontinuously.B.7.7%compoundeddaily.C.8.0%compoundedsemiannually.正確答案：C參考解析：Ciscorrect,asshowninthefollowing(whereFVisfuturevalueandPVispresentvalue):[單選題]18.ThefollowingtableshowstheannualreturnsforFundY.

ThegeometricmeanforFundYisclosestto:A.14.9%.B.15.6%.C.19.5%.正確答案：A參考解析：Aiscorrect.ThegeometricmeanreturnforFundYisfoundasfollows:FundY=[(1＋0.195)×(1–0.019)×(1＋0.197)×(1＋0.350)×(1＋0.057)]^(1/5)–1=14.9%.[單選題]19.Ahypothesistestforanormally-distributedpopulationata0.05significancelevelimpliesa:A.95%probabilityofrejectingatruenullhypothesis.B.95%probabilityofaTypeIerrorforatwo-tailedtest.C.5%criticalvaluerejectionregioninatailofthedistributionforaone-tailedtest.正確答案：C參考解析：Ciscorrect.Foraone-tailedhypothesistest,thereisa5%criticalvaluerejectionregioninonetailofthedistribution.[單選題]20.Theprobabilitydistributionforacompany‘ssalesis:

Thestandarddeviationofsalesisclosestto:A.$9.81million.B.$12.20million.C.$32.40million.正確答案：A參考解析：Aiscorrect.Theanalystmustfirstcalculateexpectedsalesas0.05×$70+0.70×$40+0.25×$25=$3.50million+$28.00million+$6.25million=$37.75million.Aftercalculatingexpectedsales,wecancalculatethevarianceofsales:

Thestandarddeviationofsalesisthusσ=($96.18)^1/2=$9.81million.[單選題]21.Inadiscreteuniformdistributionwith20potentialoutcomesofintegers1to20,theprobabilitythatXisgreaterthanorequalto3butlessthan6,P(3≤X＜6),is:A.0.10.B.0.15.C.0.20.正確答案：B參考解析：Biscorrect.Theprobabilityofanyoutcomeis0.05,P(1)=1/20=0.05.TheprobabilitythatXisgreaterthanorequalto3butlessthan6,whichisexpressedasP(3≤X＜6)=P(3)+P(4)+P(5)=0.05+0.05+0.05=0.15[單選題]22.Thelevelofsignificanceofahypothesistestisbestusedto:A.calculatetheteststatistic.B.definethetest’srejectionpoints.C.specifytheprobabilityofaTypeIIerror.正確答案：B參考解析：Biscorrect.Thelevelofsignificanceisusedtoestablishtherejectionpointsofthehypothesistest.[單選題]23.Afterestimatingtheprobabilitythataninvestmentmanagerwillexceedhisbenchmarkreturnineachofthenexttwoquarters,ananalystwantstoforecasttheprobabilitythattheinvestmentmanagerwillexceedhisbenchmarkreturnoverthetwo-quarterperiodintotal.Assumingthateachquarter’sperformanceisindependentoftheother,whichprobabilityruleshouldtheanalystselect?A.AdditionruleB.MultiplicationruleC.Totalprobabilityrule正確答案：B參考解析：Biscorrect.Becausetheeventsareindependent,themultiplicationruleismostappropriateforforecastingtheirjointprobability.ThemultiplicationruleforindependenteventsstatesthatthejointprobabilityofbothAandBoccurringisP(AB)=P(A)P(B).[單選題]24.WhichofthefollowingisaTypeIerror?A.RejectingatruenullhypothesisB.RejectingafalsenullhypothesisC.Failingtorejectafalsenullhypothesis正確答案：A參考解析：Aiscorrect.ThedefinitionofaTypeIerroriswhenatruenullhypothesisisrejected.[單選題]25.Amanagerwillselect20bondsoutofhisuniverseof100bondstoconstructaportfolio.Whichformulaprovidesthenumberofpossibleportfolios?A.PermutationformulaB.MultinomialformulaC.Combinationformula正確答案：C參考解析：Ciscorrect.Thecombinationformulaprovidesthenumberofwaysthatrobjectscanbechosenfromatotalofnobjects,whentheorderinwhichtherobjectsarelisteddoesnotmatter.Theorderofthebondswithintheportfoliodoesnotmatter.[單選題]26.Whichofthefollowingstatementsonp-valueiscorrect?A.Thep-valueisthesmallestlevelofsignificanceatwhichH0canberejected.B.Thep-valueindicatestheprobabilityofmakingaTypeIIerror.C.Thelowerthep-value,theweakertheevidenceforrejectingtheH0.正確答案：A參考解析：Aiscorrect.Thep-valueisthesmallestlevelofsignificance(α)atwhichthenullhypothesiscanberejected.[單選題]27.Forasamplesizeof65withameanof31takenfromanormallydistributedpopulationwithavarianceof529,a99%confidenceintervalforthepopulationmeanwillhavealowerlimitclosestto:A.23.64.B.25.41.C.30.09.正確答案：A參考解析：Aiscorrect.Tosolve,usethestructureofConfidenceinterval=Pointestimate±Reliabilityfactor×Standarderror,which,foranormallydistributedpopulationwithknownvariance,isrepresentedbythefollowingformula:[單選題]28.Whichofthefollowinggroupsbestillustratesapopulation?A.The500companiesintheS&P500IndexB.TheNYSE-listedstocksintheDowJonesIndustrialAverageC.TheLehmanAggregateBondIndexasarepresentationoftheUSbondmarket正確答案：A參考解析：Aiscorrect.Apopulationisdefinedasallmembersofaspecifiedgroup.TheS&P500Indexconsistsof500companies,sothisgroupisthepopulationofcompaniesintheindex.BisincorrectbecausethereareseveralDowJonescomponentstocksthatarenottradedontheNYSE,makingtheNYSEgroupasubsetofthetotalpopulationofstocksincludedintheDowJonesaverage.CisincorrectbecausealthoughtheLehmanAggregateBondIndexisrepresentativeoftheUSbondmarket,itisasamplingofbondsinthatmarketandnottheentirepopulationofbondsinthatmarket.[單選題]29.Aclientrequires￡100,000oneyearfromnow.Ifthestatedannualrateis2.50%compoundedweekly,thedepositneededtodayisclosestto:A.￡97,500.B.￡97,532.C.￡97,561.正確答案：B參考解析：Biscorrectbecause￡97,531representsthepresentvalue(PV)of￡100,000receivedoneyearfromtodaywhentoday’sdepositearnsastatedannualrateof2.50%andinterestcompoundsweekly,asshowninthefollowingequation(whereFVisfuturevalue):[單選題]30.Foralumpsuminvestmentof￥250,000investedatastatedannualrateof3%compoundeddaily,thenumberofmonthsneededtogrowthesumto￥1,000,000isclosestto:A.555.B.563.C.576.正確答案：A參考解析：Aiscorrect.Theeffectiveannualrate(EAR)iscalculatedasfollows:

SolvingforNonafinancialcalculatorresultsin(whereFVisfuturevalueandPVispresentvalue):[單選題]31.Anestimatorwithanexpectedvalueequaltotheparameterthatitisintendedtoestimateisdescribedas:A.efficient.B.unbiased.C.consistent.正確答案：B參考解析：Biscorrect.Anunbiasedestimatorisoneforwhichtheexpectedvalueequalstheparameteritisintendedtoestimate.[單選題]32.Asaverdepositsthefollowingamountsinanaccountpayingastatedannualrateof4%,compoundedsemiannually:

AttheendofYear4,thevalueoftheaccountisclosestto:A.$30,432B.$30,447C.$31,677正確答案：B參考解析：Biscorrect.Tosolveforthefuturevalueofunequalcashflows,computethefuturevalueofeachpaymentasofYear4atthesemiannualrateof2%,andthensumtheindividualfuturevalues,asfollows:[單選題]33.Astockispricedat$100.00andfollowsaone-periodbinomialprocesswithanupmovethatequals1.05andadownmovethatequals0.97.If1millionBernoullitrialsareconducted,andtheaverageterminalstockpriceis$102.00,theprobabilityofanupmove(p)isclosestto:A.0.375.B.0.500.C.0.625.正確答案：C參考解析：Ciscorrect.Theprobabilityofanupmove(p)canbefoundbysolvingtheequation:(p)uS＋(1–p)dS=(p)105＋(1–p)97=102.Solvingforpgives8p=5,sothatp=0.625.[單選題]34.IftheprobabilitythatZolafCompanysalesexceedlastyear'ssalesis0.167,theoddsforexceedingsalesareclosestto:A.1to5.B.1to6.C.5to1.正確答案：A參考解析：Aiscorrect.GivenoddsforEofatob,theimpliedprobabilityofE=a/(a+b).Statedintermsofoddsatobwitha=1,b=5,theprobabilityofE=1/(1+5)=1/6=0.167.Thisresultconfirmsthataprobabilityof0.167forbeatingsalesisoddsof1to5.[單選題]35.Givenastatedannualinterestrateof6%compoundedquarterly,thelevelamountthat,depositedquarterly,willgrowto￡25,000attheendof10yearsisclosestto:A.￡461.B.￡474.C.￡836.正確答案：A參考解析：Aiscorrect.Tosolveforanannuity(A)payment,whenthefuturevalue(FV),interestrate,andnumberofperiodsisknown,usethefollowingequation:[單選題]36.Aportfoliomanagerannuallyoutperformsherbenchmark60%ofthetime.Assumingindependentannualtrials,whatistheprobabilitythatshewilloutperformherbenchmarkfourormoretimesoverthenextfiveyears?A.0.26B.0.34C.0.48正確答案：B參考解析：Biscorrect.Tocalculatetheprobabilityof4yearsofoutperformance,usetheformula:

Usingthisformulatocalculatetheprobabilityin4of5years,n=5,x=4andp=0.60.Therefore,

Theprobabilityofoutperforming4ormoretimesisp(4)+p(5)=0.2592+0.0778=0.3370[單選題]37.Incontrasttonormaldistributions,lognormaldistributions:A.areskewedtotheleft.B.haveoutcomesthatcannotbenegative.C.aremoresuitablefordescribingassetreturnsthanassetprices.正確答案：B參考解析：Biscorrect.Bydefinition,lognormalrandomvariablescannothavenegativevalues.[單選題]38.Whichofthefollowingisapropertyoftwodependentevents?A.Thetwoeventsmustoccursimultaneously.B.Theprobabilityofoneeventinfluencestheprobabilityoftheotherevent.C.Theprobabilityofthetwoeventsoccurringistheproductofeachevent’sprobability.正確答案：B參考解析：Biscorrect.Theprobabilityoftheoccurrenceofoneisrelatedtotheoccurrenceoftheother.Ifwearetryingtoforecastoneevent,informationaboutadependenteventmaybeuseful.[單選題]39.Theannualreturnsforthreeportfoliosareshowninthefollowingtable.PortfoliosPandRwerecreatedinYear1,PortfolioQinYear2.

Themedianannualreturnfromportfoliocreationtoyear5for:A.PortfolioPis4.5%.B.PortfolioQis4.0%.C.PortfolioRishigherthanitsarithmeticmeanannualreturn.正確答案：C參考解析：Ciscorrect.ThemedianofPortfolioRis0.8%higherthanthemeanforPortfolioR.[單選題]40.Anincreaseinsamplesizeismostlikelytoresultina:A.widerconfidenceinterval.B.decreaseinthestandarderrorofthesamplemean.C.lowerlikelihoodofsamplingfrommorethanonepopulation.正確答案：B參考解析：Biscorrect.Allelsebeingequal,asthesamplesizeincreases,thestandarderrorofthesamplemeandecreasesandthewidthoftheconfidenceintervalalsodecreases.[單選題]41.Twoportfolioshaveunimodalreturndistributions.Portfolio1hasaskewnessof0.77,andPortfolio2hasaskewnessof–1.11.Whichofthefollowingiscorrect?A.ForPortfolio1,themedianislessthanthemean.B.ForPortfolio1,themodeisgreaterthanthemean.C.ForPortfolio2,themeanisgreaterthanthemedian.正確答案：A參考解析：Aiscorrect.Portfolio1ispositivelyskewed,sothemeanisgreaterthanthemedian,whichisgreaterthanthemode.[單選題]42.Arandomnumberbetweenzeroandoneisgeneratedaccordingtoacontinuousuniformdistribution.Whatistheprobabilitythatthefirstnumbergeneratedwillhaveavalueofexactly0.30?A.0%B.30%C.70%正確答案：A參考解析：Aiscorrect.Theprobabilityofgeneratingarandomnumberequaltoanyfixedpointunderacontinuousuniformdistributioniszero.[單選題]43.Areturndistributionwithfrequentsmallgainsandafewextremelossesismostlikelytobecalled:A.leptokurtic.B.positivelyskewed.C.negativelyskewed.正確答案：C參考解析：Ciscorrect.Areturndistributionwithnegativeskewhasfrequentsmallgainsandafewextremelosses.Aisincorrectbecausealeptokurticdistributionismorepeakedwithfattertails,whichexhibitbothextremegainsandlosses.Bisincorrectbecauseareturndistributionwithpositiveskewhasfrequentsmalllossesandafewextremegains.[單選題]44.Givenaportfoliooffivestocks,howmanyuniquecovarianceterms,excludingvariances,arerequiredtocalculatetheportfolioreturnvariance?A.10B.20C.25正確答案：A參考解析：Aiscorrect.Acovariancematrixforfivestockshas5×5=25entries.Subtractingthe5diagonalvariancetermsresultsin20off-diagonalentries.Becauseacovariancematrixissymmetrical,only10entriesareunique(20/2=10).[單選題]45.Amanagerinvests€5,000annuallyinasecurityforfouryearsatthepricesshowninthefollowingtable.

Theaveragepricepaidforthesecurityisclosestto:A.€76.48.B.€77.26.C.€78.00.正確答案：A參考解析：Aiscorrect.Theharmonicmeanisappropriatefordeterminingtheaveragepriceperunit.Itiscalculatedbysummingthereciprocalsoftheprices;thenaveragingthatsumbydividingbythenumberofprices;andfinally,takingthereciprocaloftheaverage:4/[(1/62.00)+(1/76.00)+(1/84.00)+(1/90.00)]=€76.48.[單選題]46.Thepresentvalue(PV)ofaninvestmentwiththefollowingyear-endcashflows(CF)anda12%requiredannualrateofreturnisclosestto:

CF1=100,000eurodollarforyear1;CF2=150,000eurodollarforyear2;CF3=CF4=0eurodollarforyear3&4;CF5=-10,000eurodollarforyear5.A.€201,747.B.€203,191.C.€227,573.正確答案：B參考解析：Biscorrect,asshowninthefollowingtable.[單選題]47.Ananalystisusingthedatainthefollowingtabletoprepareastatisticalreport.

Thecumulativerelativefrequencyfortheinterval-1.71%≤x＜2.03%isclosestto:A.0.250.B.0.333.C.0.583.正確答案：C參考解析：Ciscorrect.Thecumulativerelativefrequencyofanintervalidentifiesthefractionofobservationsthatarelessthantheupperlimitofthegiveninterval.Itisdeterminedbysummingtherelativefrequenciesfromthelowestintervaluptoandincludingthegiveninterval.Thefollowingexhibitshowstherelativefrequenciesforalltheintervalsofthedatafromthepreviousexhibit:

Theinterval-1.71%≤x＜2.03%hasacumulativerelativefrequencyof0.583.[單選題]48.Amutualfundhasthereturnfrequencydistributionshowninthefollowingtable.

Whichofthefollowingstatementsiscorrect?A.Therelativefrequencyoftheinterval“–1.0to+2.0”is20%.B.Therelativefrequencyoftheinterval“+2.0to+5.0”is23%.C.Thecumulativerelativefrequencyoftheinterval“+5.0to+8.0”is91.7%.正確答案：A參考解析：Aiscorrect.Therelativefrequencyistheabsolutefrequencyofeachintervaldividedbythetotalnumberofobservations.Here,therelativefrequencyiscalculatedas:(12/60)×100=20%.Bisincorrectbecausetherelativefrequencyofthisintervalis(23/60)×100=38.33%.Cisincorrectbecausethecumulativerelativefrequencyofthelastintervalmustequal100%.[單選題]49.Lastyear,aninvestorallocatedhisretirementsavingsintheassetclassesshowninthefollowingtable.

Theportfolioreturnforlastyearisclosestto:A.5.1%.B.5.3%.C.6.3%.正確答案：C參考解析：Ciscorrect.Theportfolioreturnmustbecalculatedastheweightedmeanreturn,wheretheweightsaretheallocationsineachassetclass:(0.20×8%)＋

(0.40×12%)＋【0.25×(-3%)】＋(0.15×4%)=6.25%,or≈6.3%.[單選題]50.Whichofthefollowingrepresentsacorrectstatementaboutthep-value?A.Thep-valueofferslesspreciseinformationthandoestherejectionpointsapproach.B.Alargerp-valueprovidesstrongerevidenceinsupportofthealternativehypothesis.C.Ap-valuelessthanthespecifiedlevelofsignificanceleadstorejectionofthenullhypothesis.正確答案：C參考解析：Ciscorrect.Thep-valueisthesmallestlevelofsignificanceatwhichthenullhypothesiscanberejectedforagivenvalueoftheteststatistic.Thenullhypothesisisrejectedwhenthep-valueislessthanthespecifiedsignificancelevel.[單選題]51.Frequencydistributionssummarizedatain:A.atabulardisplay.B.overlappingintervals.C.arelativelylargenumberofintervals.正確答案：A參考解析：Aiscorrect.Afrequencydistributionisatabulardisplayofdatasummarizedintoarelativelysmallnumberofintervals.Bisincorrectbecauseintervalscannotoverlap.Eachobservationisplaceduniquelyintooneinterval.Cisincorrectbecauseafrequencydistributionissummarizedintoarelativelysmallnumberofintervals.[單選題]52.Foratwo-sidedconfidenceinterval,anincreaseinthedegreeofconfidencewillresultin:A.awiderconfidenceinterval.B.anarrowerconfidenceinterval.C.nochangeinthewidthoftheconfidenceinterval.正確答案：A參考解析：Aiscorrect.Asthedegreeofconfidenceincreases(e.g.,from95%to99%),agivenconfidenceintervalwillbecomewider.Aconfidenceintervalisarangeforwhichonecanassertwithagivenprobability1–α,calledthedegreeofconfidence,thatitwillcontaintheparameteritisintendedtoestimate.[單選題]53.Whichofthefollowingsequencesbestrepresentstherelativesizesofthemean,median,andmodeforapositivelyskewedunimodaldistribution?A.mode≤median≤meanB.mode<median<meanC.mean<median<mode正確答案：B參考解析：Biscorrect.Forthepositivelyskewedunimodaldistribution,themodeislessthanthemedian,whichislessthanthemean.Aisincorrectbecause,forthepositivelyskewedunimodaldistribution,themodeislessthanthemedian(notlessthanorequalto),whichislessthan(notlessthanorequalto)themean.Cisincorrectbecause,forthenegatively(notpositively)skewedunimodaldistribution,themeanislessthanthemedian,whichislessthanthemode.[單選題]54.WhichofthefollowingeventscanberepresentedasaBernoullitrial?A.TheflipofacoinB.TheclosingpriceofastockC.Thepickingofarandomintegerbetween1and10正確答案：A參考解析：Aiscorrect.Atrial,suchasacoinflip,willproduceoneoftwooutcomes.SuchatrialisaBernoullitrial.[單選題]55.Whichofthefollowingbestdescribeshowananalystwouldestimatetheexpectedvalueofafirmunderthescenariosofbankruptcyandsurvivorship?Theanalystwoulduse:A.theadditionrule.B.conditionalexpectedvalues.C.thetotalprobabilityruleforexpectedvalue.正確答案：C參考解析：Ciscorrect.Thetotalprobabilityruleforexpectedvalueisusedtoestimateanexpectedvaluebasedonmutuallyexclusiveandexhaustivescenarios.[單選題]56.Allelseequal,isspecifyingasmallersignificancelevelinahypothesistestlikelytoincreasetheprobabilityofaTypeIerrororTypeIIerror?A.TypeIerror(No)orTypeIIerror(No)B.TypeIerror(No)orTypeIIerror(Yes)C.TypeIerror(Yes)orTypeIIerror(No)正確答案：B參考解析：Biscorrect.SpecifyingasmallersignificanceleveldecreasestheprobabilityofaTypeIerror(rejectingatruenullhypothesis),butincreasestheprobabilityofaTypeIIerror(notrejectingafalsenullhypothesis).Asthelevelofsignificancedecreases,thenullhypothesisislessfrequentlyrejected.[單選題]57.Ata5%interestrateperyearcompoundedannually,thepresentvalue(PV)ofa10-yearordinaryannuitywithannualpaymentsof$2,000is$15,443.47.ThePVofa10-yearannuityduewiththesameinterestrateandpaymentsisclosestto:A.$14,708.B.$16,216.C.$17,443.正確答案：B參考解析：Biscorrect.Thepresentvalueofa10-yearannuity(A)duewithpaymentsof$2,000ata5%discountrateiscalculatedasfollows:

Alternatively,thePVofa10-yearannuitydueissimplythePVoftheordinaryannuitymultipliedby1.05:[單選題]58.Areportonlong-termstockreturnsfocusedexclusivelyonallcurrentlypubliclytradedfirmsinanindustryismostlikelysusceptibleto:A.look-aheadbias.B.survivorshipbias.C.intergenerationaldatamining.正確答案：B參考解析：Biscorrect.Areportthatusesacurrentlistofstocksdoesnotaccountforfirmsthatfailed,merged,orotherwisedisappearedfromthepublicequitymarketinpreviousyears.Asaconsequence,thereportisbiased.Thistypeofbiasisknownassurvivorshipbias.[單選題]59.Ananalystdevelopsthefollowingcovar