经济计量学精要v2-gujarati1yao1

3234(1)(2)2(3)t(4)F44333242.12.1.1iXi=1n(i=n)XiXiX2.1.21.k:XX∑Xi∑Xi=X1i=1i=n∑+X2+L+Xn2215nnn=4k=32.k3.4.ab1232.22.2.1(statisticalorrandomexperiment)12.2.2populationorsamplespace4(a∑+bXi)=na+bXi∑(Xi∑+Yi)=Xi∑+Yi∑kXi∑=kXi∑3=4×3=12i=14∑k=nki=1i=n∑123456(1000)(10070)2.1HTHHHTTHTTHHHT2.21PaulNewbold,StatisticsforBusinessandEconomics,4thed.,Prentic-Hall,EnglewoodCliffs,N.J.,1995,p.75.4O1O2O3O42.2.3(samplepoint)2.2HHHTTHTT2.3O1O2O3O42.2.4(events)(mutuallyexclusive)2.3O1(equallylikely)(collectivelyexhaustive)HHHTTHTT2.3O1O2O3O419892.3A16O1OO3O42.3A2.2HTTHA(HTTHHHHTTHTT)BHHB(HHHHHTTHTT)2.42.2HHHTTHTT1TT0TH1TH1HT1HH22.51*1=0.254m217stochasticorrandomvariabler.vr.v30122.33012XYZX1X2X3(discreterandomvariable)012012(continuousrandomvariable)60722.42.4.1nAmA(probability)P(A)(2-1)(1)(2)1/2HT521/5213/52(prioridefinition)1/21PA=_mn=A1234561/6m=1n=62.6120002.4.22-1200(1)(2)(3)(4)=(3)/200095001019150020292500303935100.050404945200.100505955350.175606965500.250707975450.225808985300.150909995__10_______0.0502001.0nnmAnAPAm/n12-14(1)01A0PA12-2PA=0APA=1A012-1(2)ABCPA+B+C+=PA+PB+PC+2-33.ABC1182-12002-1(frequencydistribution)3(absolutefrequencies)4(relativefrequencies)(200)7079450.225,452002.71219PA+B+C+=PA+PB+PC+=12-4(1)ABCPABC=PAPBPC2-5PABCABCPABCjointprobabilityPAPBPC(unconditional)(marginal)(individual)2-6(2)ABC2-5ABPA+B=PA+PBPAB2-6PABABABPAB=02-32-6ABBABAconditionalprobabilityPABPAB=2-7BAABBPBA=2-8P(AB)P(A)P(AB)P(B)2.61/6123456P(1+2+3+4+5+6)=1P(1+2+3+4+5+6)=P(1)+P(2)++P(6)=1/6+1/6+1/6+1/6+1/6+1/6=12.8ABP(AB)P(AB)=P(A)P(B)=(1/2)(1/2)=1/41/22.94P()=P()+P()P()=13/52+4/521/52=4/132.10ABPABPAB===0.625PA=300/500=0.60.60.62512.4.32.5GNP2.5XPDF2.5.1(PDF)2.5(100/500)(160/500)P(AB)P(B)20500300200100602.11XX3012X01/4()41TT1/4HTTH2/4=1/22.12PDFXf(X)01/411/221/4_______1.001A,BP(AB)=P(A)P(B)P(A|B)==P(A)P(B)/P(B)=P(A)ABP(AB)P(B)221Xf(X)(probabilitydistributionorprobabilitydensityfunctionPDF)XXPDF(PDFofadiscreterandomvariable)1(2.43)f(X)i=1,2,3,nXxi2-9P(X=xi)XxiPX=222-12-1(2.12)2.5.2PDFofacontinuousrandomvariableX60682-212-2606863062.563.52.5.3XFXcumulativedistribution=P(X=xi)0⎧⎨⎩60682-21functionCDFFX=PXX2-10PXXXx0PX2X2Xx2-11XxX25/16X311/16X41f(X)x∑F(X)=f(X)x∑224()PDFCDFXf(x)(PDF)Xf(x)(CDF)00X11/16X01/1611X24/16X15/1622X36/16X211/1633X44/16X315/1644X51/16X412.132-3(2.13)2-42232-32.132.13(stepfunction)2-42.62.122.13(multivariableprobabilitydistributions)2-2(X)(Y)(X)123(Y)()(Bbb)(Bb)(B)8.513501811.521421817.5011314152015502-3(X)123(Y)()(Bbb)(Bb)(B)8.50.260.100.000.3611.50.040.280.040.3617.50.000.020.260.280.300.400.301.00XY1313B8.51422B11.52-2XY2-250502-32-3(bivariateorjointprobabilitydensityfunction,orjointPDF)(jointprobability)X2Y11.5f(X,Y)XYXYf(X,Y)=P(X=x,Y=y)(2-12)=0Xx,Yy2-250(X)(Y)XX=1(Bbb)X=2(Bb),X=3(B)Bbb,Bb,BBbBBbbBb2.1424XxYyxyX3Y17.50.262.6.1f(X),f(Y)fXYfXYf(X)f(Y)(univariate,unconditional,individual,ormarginalPDFsX2YXX2-3X10.30YX20.40YX30.30YX2-4Yf(X)[f(Y)]12-4XYX()f(X)Y()f(Y)10.308.50.3620.4011.50.3630.3017.50.281.001.00XX2-32-3Y2.6.218.5X=1Y=8.5(conditionalprobability)(conditionalprobabilitydensityfunction)fYX)=P(Y=yX=x)(2-13)f(YX)YX=x1Yy8.5Xf(XY)=P(X=xY=y)(2-14)f(XY)=(2-15)=f(Y|X)=(2-16)=XYXf(X,Y)f(X)XYYf(X,Y)f(Y)225[BAP(XY)]f(Y=8.5X=1),f(Y=8.5X=1)0.26/0.302-30.86672-3Y8.50.361Y8.50.872.6.3independentrandomvariablesf(X=1,Y=1),f(X=1),f(Y=1)2-51/91/31/3(statisticallyindependence)XYf(X,Y)=f(X)f(Y)2-172-5XYXY2-172-5Xf(Y)12311/91/91/93/9Y21/91/91/93/931/91/91/93/9f(X)3/93/93/91f(Y=8.5,X=1)f(X=1)123()XY2-52.152.14(2-17)X=1(Bbb)Y=8.52-3f(X=1,Y=8.5)=0.26;f(X=1)=0.30,f(Y=8.5)=0.360.26(0.30)(0.36)()2.162.72.122.7.1(expectedvalue)E(X)X2-18f(X)XX1(populationmeanvalue)()2-183.51234563.53.5342-5X∑E(X)=Xf(X)X∑262.62-62.172-6(1)(2)(3)Xf(X)Xf(X)11/61/621/62/631/63/641/64/651/65/661/66/6E(X)=21/6=3.51/62-5(2.17)E(X)1∑∫227(1)bE(b)=b(2-19)b=2,E(2)=2(2)8XYE(X+Y)=E(X)+E(Y)(2-20)(3)E(X/Y)(2-21)(4)E(XY)E(X)E(Y)(2-22)XYE(XY)=E(X)E(Y)(2-23)XYf(X,Y)=f(X)f(Y)XY(5)aE(aX)=aE(X)(2-24)(6)a,bE(aX+b)=aE(X)+E(b)=aE(X)+b(2-25)(1)(2)(5)E(4X+7)=4E(X)+72.7.2(variance)E(X)E(Y)2-4X1(0.30)+2(0.40)+3(0.30)=2.02Bb2.182-4Y()8.5(0.36)+11.5(0.36)+17.5(0.28)=12.102.191E(X+Y+Z+W)=E(X)+E(Y)+E(Z)=E(W)XE(X)ux(u)var(X)=x2=E(Xux)2(2-26)x2(2-26)XXE(X)X2-6()2-6x2x(standarddeviation,s.d).(2-26)X(2-27)(2-27)XX2-7XXf(X)(Xux)2f(X)11/6(13.5)2(1/6)21/6(23.5)2(1/6)31/6(33.5)2(1/6)41/6(43.5)2(1/6)51/6(53.5)2(1/6)61/6(63.5)2(1/6)=2.9167var(X)=(X-ux)X∑2f(X)282.17()3.52-72.202292.91671.7078(1)(2)XYvar(X+Y)=var(X)+var(Y)(2-28)var(XY)=var(X)+var(Y)(3)bvar(X+b)=var(X)(2-29)var(X+7)=var(X)(4)avar(aX)=a2var(X)(2-30)var(5X)=25var(X)(5)a,bvar(aX+b)=a2var(X)(2-31)(3)(4)var(5X+9)=25var(X)(6)XYa,bvar(aX+bY)=a2var(X)+b2var(Y)(2-32)var(3X+5Y)=9var(X)+25var(Y)2.7.3(2.14)(characteristicsofmultivariateDDFs)(covariance)(correlation)XYuxuycov(X,Y)=E[(Xux)(Yuy)](2-33)=E(XY)uxuy(2-33)(2-33)XY(2-34)()2.21()cov(X,Y)=(X-ux)Y∑X∑(Y-uy)f(X,Y)=XYf(X,Y)-uxuyY∑X∑(1)XYE(XY)=E(X)E(Y)=uxuy(2-35)(2-33)(2)cov(a+bX,c+dY)=bdcov(X,Y)(2-36),a,b,c,d(3)cov(X,X)=var(X)(2-37)2.7.4+2.342.34()(2-38)(2-38)1.(1)(2)11=cov(X,Y)σxσy302.14