斯托克、沃森着《计量经济学》(第二版)答案

PARTONESolutionstoExercisesChapter2ReviewofProbability„SolutionstoExercises1.(a)ProbabilitydistributionfunctionforYOutcome(numberofheads)Y0Y1Y2probability0.250.500.25(b)CumulativeprobabilitydistributionfunctionforYOutcome(numberofheads)Y00dY11dY2Yt2Probability00.250.751.0(c)=()(00.25)(10.50)(20.25)1.00YEYPuuuUsingKeyConcept2.3:22var()()[()],YEYEYanduuu2222()(00.25)(10.50)(20.25)1.50EYsothat222var()()[()]1.50(1.00)0.50.YEYEY2.WeknowfromTable2.2thatPr(0)022,YPr(1)078,YPr(0)030,XPr(1)070.XSo(a)()0Pr(0)1Pr(1)00221078078,()0Pr(0)1Pr(1)00301070070YXEYYYEXXXPPuuuuuuuu(b)222222222222[()](00.70)Pr(0)(10.70)Pr(1)(070)030030070021[()](00.78)Pr(0)(10.78)Pr(1)(078)02202207801716XXYYEXXXEYYYVPVPuuuuuuuu4Stock/Watson-IntroductiontoEconometrics-SecondEdition(c)Table2.2showsPr(0,0)015,XYPr(0,1)015,XYPr(1,0)007,XYPr(1,1)063.XYSocov(,)[()()](0-0.70)(0-0.78)Pr(0,0)(0070)(1078)Pr(01)(1070)(0078)Pr(10)(1070)(1078)Pr(11)(070)(078)015(070)022015030(078)0070XYXYXYEXYXYXYXYXYVPPuuuuuu300220630084,0084(,)0442502101716XYXYcorXYVVVuuu3.Forthetwonewrandomvariables36WXand207,VYwehave:(a)()(207)207()2070781454,()(36)36()3607072EVEYEYEWEXEXuu(b)222222var(36)636021756,var(207)(7)490171684084WXVYXYVVVV˜u˜u(c)(36,207)6(7)(,)42008435283528(,)0442575684084WVWVWVcovXYcovXYcorWVVVVVuu4.(a)uu333()0(1)1EXppp(b)uu()0(1)1kkkEXppp(c)()0.3EX22var()()[()]0.30.090.21XEXEXThus,0.210.46.VTocomputetheskewness,usetheformulafromexercise2.21:332323()()3[()][()]2[()]0.330.320.30.084EXEXEXEXEXPuuAlternatively,uu333()=[(10.3)0.3][(00.3)0.7]0.084EXPThus,skewness333()/.084/0.460.87.EXPVSolutionstoExercisesinChapter25Tocomputethekurtosis,usetheformulafromexercise2.21:443224234()()4[()][()]6[()][()]3[()]0.340.360.330.30.0777EXEXEXEXEXEXEXPuuuAlternatively,uu444()=[(10.3)0.3][(00.3)0.7]0.0777EXPThus,kurtosisis444()/=.0777/0.461.76EXPV5.LetXdenotetemperatureinqFandYdenotetemperatureinqC.RecallthatY0whenX32andY100whenX212;thisimplies(100/180)(32)or17.78(5/9).YXYXuuUsingKeyConcept2.3,q70FXPimpliesthat17.78(5/9)7021.11C,YPuqandq7FXVimplies(5/9)73.89C.YVuq6.ThetableshowsthatPr(0,0)0045,XYPr(0,1)0709,XYPr(1,0)0005,XYPr(1,1)0241,XYPr(0)0754,XPr(1)0246,XPr(0)0050,YPr(1)0950.Y(a)uuuu()0Pr(0)1Pr(1)00050109500950YEYYYP(b)(unemployed)UnemploymentRate(laborforce)Pr(0)0050109501()##YEY(c)Calculatetheconditionalprobabilitiesfirst:Pr(0,0)0045Pr(0|0)00597,Pr(0)0754XYYXXPr(0,1)0709Pr(1|0)09403,Pr(0)0754XYYXXPr(1,0)0005Pr(0|1)00203,Pr(1)0246XYYXXPr(1,1)0241Pr(1|1)09797Pr(1)0246XYYXXTheconditionalexpectationsare(|1)0Pr(0|1)1Pr(1|1)00020310979709797,(|0)0Pr(0|0)1Pr(1|0)00059710940309403EYXYXYXEYXYXYXuuuuuuuu6Stock/Watson-IntroductiontoEconometrics-SecondEdition(d)Usethesolutiontopart(b),Unemploymentrateforcollegegrads1(|1)10.97970.0203.Unemploymentratefornon-collegegrads1(|0)10.94030.0597.EYXEYX(e)TheprobabilitythatarandomlyselectedworkerwhoisreportedbeingunemployedisacollegegraduateisPr(1,0)0005Pr(1|0)01Pr(0)0050XYXYYTheprobabilitythatthisworkerisanon-collegegraduateisPr(0|0)1Pr(1|0)10109XYXY(f)Educationalachievementandemploymentstatusarenotindependentbecausetheydonotsatisfythat,forallvaluesofxandy,Pr(|)Pr()YyXxYyForexample,Pr(0|0)00597Pr(0)0050YXYz7.Usingobviousnotation,;CMFthusCMFPPPand2222cov(,).CMFMFVVVThisimplies(a)4045$85,000CPperyear.(b)(,)(,),MFCovMFcorMFVVsothat(,)(,).MFCovMFcorMFVVThus(,)12180.80172.80,CovMFuuwheretheunitsaresquaredthousandsofdollarsperyear.(c)2222cov(,),CMFMFVVVsothat22212182172.80813.60,CVuand813.6028.524CVthousanddollarsperyear.(d)FirstyouneedtolookupthecurrentEuro/dollarexchangerateintheWallStreetJournal,theFederalReservewebpage,orotherfinancialdataoutlet.Supposethatthisexchangerateise(saye0.80eurosperdollar);each1$isthereforewitheE.ThemeanisthereforeePC(inunitsofthousandsofeurosperyear),andthestandarddeviationiseVC(inunitsofthousandsofeurosperyear).Thecorrelationisunit-free,andisunchanged.8.()1,YEYP2var()4.YYVWith12(1),ZY22111(1)(1)(11)0,222111var(1)41244ZYZYEYYPPVV§·¨¸©¹§·u¨¸©¹SolutionstoExercisesinChapter279.ValueofY1422304065ProbabilityDistributionofX10.020.050.100.030.010.2150.170.150.050.020.010.40ValueofX80.020.030.150.100.090.39ProbabilitydistributionofY0.210.230.300.150.111.00(a)Theprobabilitydistributionisgiveninthetableabove.22222222()140.21220.23300.30400.15650.1130.15()140.21220.23300.30400.15650.111127.23Var(Y)()[()]218.2114.77YEYEYEYEYVuuuuuuuuuu(b)ConditionalProbabilityofY|X8isgiveninthetablebelowValueofY14223040650.02/0.390.03/0.390.15/0.390.10/0.390.09/0.39(|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)39.21EYXuuuuu222222(|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)1778.7EYXuuuuu28Var()1778.739.21241.6515.54YXYV_(c)()(1140.02)(122:0.05)(8650.09)171.7EXYuuuuuLCov(,)()()()171.75.3330.1511.0XYEXYEXEYuCorr(,)Cov(,)/()11.0/(5.4614.77)0.136XY