计量经济学(斯托克-沃森-第三版)答案

ForStudentsSolutionstoOdd-NumberedEnd-of-ChapterExercises©2011PearsonEducation,Inc.PublishingasAddisonWesleyChapter2ReviewofProbability2.1.(a)ProbabilitydistributionfunctionforYOutcome(numberofheads)Y0Y1Y2Probability0.250.500.25(b)CumulativeprobabilitydistributionfunctionforYOutcome(numberofheads)Y00Y11Y2Y2Probability00.250.751.0(c)=()(00.25)(10.50)(20.25)1.00YEY.,.dFFqUsingKeyConcept2.3:22var()()[()],YEYEYand(|)iiuXsothat222var()()[()]1.50(1.00)0.50.YEYEY2.3.Forthetwonewrandomvariables36WXand207,VYwehave:(a)()(207)207()2070781454,()(36)36()3607072EVEYEYEWEXEX(b)222222var(36)636021756,var(207)(7)490171684084WXVYXY(c)cov(36,207)6(7)cov(,)4200843528WVXYXY3528corr(,)0442575684084WVWVWVSolutionstoOdd-NumberedEnd-of-ChapterExercises3©2011PearsonEducation,Inc.PublishingasAddisonWesley2.5.LetXdenotetemperatureinFandYdenotetemperatureinC.RecallthatY0whenX32andY100whenX212;thisimplies(100/180)(32)or17.78(5/9).YXYXUsingKeyConcept2.3,X70oFimpliesthat17.78(5/9)7021.11C,YandX7oFimplies(5/9)73.89C.Y2.7.Usingobviousnotation,;CMFthusCMFand2222cov(,).CMFMFThisimplies(a)4045$85,000Cperyear.(b)cov(,)corr(,)MFMFMF,sothatcov(,)corr(,).MFMFMFThuscov(,)MF12180.80172.80,wheretheunitsaresquaredthousandsofdollarsperyear.(c)2222cov(,),CMFMFsothat22212182172.80813.60,Cand813.6028.524Cthousanddollarsperyear.(d)FirstyouneedtolookupthecurrentEuro/dollarexchangerateintheWallStreetJournal,theFederalReservewebpage,orotherfinancialdataoutlet.Supposethatthisexchangerateise(saye0.80Eurosperdollar);each1dollaristhereforewitheEuros.ThemeanisthereforeeC(inunitsofthousandsofEurosperyear),andthestandarddeviationiseC(inunitsofthousandsofEurosperyear).Thecorrelationisunit-free,andisunchanged.ValueofY2.9.1422304065ProbabilityDistributionofX10.020.050.100.030.010.2150.170.150.050.020.010.40ValueofX80.020.030.150.100.090.39ProbabilitydistributionofY0.210.230.300.150.111.00(a)Theprobabilitydistributionisgiveninthetableabove.22222222()140.21220.23300.30400.15650.1130.15()140.21220.23300.30400.15650.111127.23var()()[()]218.2114.77YEYEYYEYEY4Stock/Watson•IntroductiontoEconometrics,ThirdEdition©2011PearsonEducation,Inc.PublishingasAddisonWesley(b)TheconditionalprobabilityofY|X8isgiveninthetablebelowValueofY14223040650.02/0.390.03/0.390.15/0.390.10/0.390.09/0.39222222(|8)14(0.02/0.39)22(0.03/0.39)30(0.15/0.39)40(0.10/0.39)65(0.09/0.39)39.21(|8)14(0.02/0.39)22(0.03/0.39)30(0.15/0.39)40(0.10/0.39)65(0.09/0.39)1778.7EYXEYX28var()1778.739.21241.6515.54YXY(c)()(1140.02)(122:0.05)(8650.09)171.7EXYcov(,)()()()171.75.3330.1511.0XYEXYEXEYcorr(,)cov(,)/()11.0/(2.6014.77)0.286XYXYXY2.11.(a)0.90(b)0.05(c)0.05(d)When210~,Ythen10,/10~.YF(e)2,YZwhere~(0,1),ZNthusPr(1)Pr(11)0.32.YZ2.13.(a)2222()Var()101;()Var()1000100.YWEYYEWW(b)YandWaresymmetricaround0,thusskewnessisequalto0;becausetheirmeaniszero,thismeansthatthethirdmomentiszero.(c)Thekurtosisofthenormalis3,so443()/YYEY;solvingyields4E()3;YasimilarcalculationyieldstheresultsforW.(d)First,conditionon0,Xsothat:SW2342.(|0)0;(|0)100,(|0)0,(|0)3100ESXESXESXESXSimilarly,234(|1)0;(|1)1,(|1)0,(|1)3.ESXESXESXESXFromthelawofiteratedexpectations2223334442()(|0)Pr(X0)(|1)Pr(1)0()(|0)Pr(X0)(|1)Pr(1)1000.0110.991.99()(|0)Pr(X0)(|1)Pr(1)0()(|0)Pr(X0)(|1)Pr(1)31000.013ESESXESXXESESXESXXESESXESXXESESXESXX10.99302.97SolutionstoOdd-NumberedEnd-of-ChapterExercises5©2011PearsonEducation,Inc.PublishingasAddisonWesley(e)()0,SESthus33()()0SESESfrompart(d).Thusskewness0.Similarly,222()()1.99,SSESESand44()()302.97.SESESThus,2kurtosis302.97/(1.99)76.52.15.(a)9.6101010.410Pr(9.610.4)Pr4/4/4/9.61010.410Pr4/4/YYnnnZnnwhereZ~N(0,1).Thus,(i)n20;9.61010.410PrPr(0.890.89)0.634/4/ZZnn(ii)n100;9.61010.410PrPr(2.002.00)0.9544/4/ZZnn(iii)n1000;9.61010.410PrPr(6.326.32)1.0004/4/ZZnn(b)10Pr(1010)Pr4/4/4/Pr.4/4/cYccYcnnnccZnnAsngetlarge4/cngetslarge,andtheprobabilityconvergesto1.(c)Thisfollowsfrom(b)andthedefinitionofconvergenceinprobabilitygiveninKeyConcept2.6.2.17.Y=0.4and20.40.60.24Y(a)(i)P(Y0.43)0.40.430.40.4PrPr0.61240.270.24/0.24/0.24/YYnnn(ii)P(Y0.37)0.40.370.40.4PrPr1.220.110.24/0.24/0.24/YYnnn(b)WeknowPr(1.96Z1.96)0.95,thuswewantntosatisfy0.410.400.411.9624/nand0.390.401.96.24/nSolvingtheseinequalitiesyieldsn9220.6Stock/Watson•IntroductiontoEconometrics,ThirdEdition©2011PearsonEducation,Inc.PublishingasAddisonWesley2.19.(a)11Pr()Pr(,)Pr(|)Pr()ljijiljiiiYyXxYyYyXxXx(b)111111()Pr()Pr(|)Pr()Pr(|)Pr()(|)Pr()iiikkljjjjiijjikljjijiliEYyYyyYyXxXxyYyXxXxEYXxXx(c)WhenXandYareindependent,Pr(,)P