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已知D(X)=9,D(Y)=4,相关系数ρXY=0.4,求D(X...

D(X+2Y)=D(X)+D(2Y)+2COV(X,2X)=D(X)+D(2Y)+4COV(X,Y)=D(X)+4D(Y)+4ρXYD(X)D(Y)=9+16+1.6*9*4=34.6D(2X-3Y)=4D(X)+9D(Y)-12ρXYD(X)D(Y)=36+36-4.8*9*4=43.2

Pxy=cov(x,y)/(DX+DY)^(1/2),可以推出cov(x,y)=12D(X-Y)=DX+DY-2COV(XY)=25+36-2*12=37

D(x+2y)=D(x)+4D(y)+2E{(x-E(x))(2y-E(2y))} =D(x)+4D(y)+4E{(x-E(x))(y-E(y))} =D(x)+4D(y)+4Cov(x,y) =D(x)+4D(y)+4ρxy*根号下(D(x)D(y)) =9+16+4*0.4*3*2 =34.6

cov(x,y)=ρXY*√D(X)*√D(Y)=0.5*3*2=3D(2X-3Y)=4 D(X)+9D(Y) -2*2*3Cov(X,Y) =36+36-12*3=36 公式:D(aX+bY)=a^2 D(X)+b^2D(Y)+ 2Cov(aX,bY)Cov(aX,bY) = ab Cov(X,Y) a,b 是常数

你好!根据定义,cov(x,y)=ρxy*√d(x)*√d(y)=0.4*2*3=2.4.经济数学团队帮你解答,请及时采纳.谢谢!

代入方程还有协方差的基本公式 D(X+Y)=D(X)+D(Y)+2COV(X,Y) 展开得到计算即可 显然这里的D(3X-2Y)展开得到=9DX+4DY-12COV(X,Y) 这里D(X)=4,D(Y)=1,ρXY=0.6 COV(X,Y)=ρXY√(DXDY) 得到9*4+4-12*0.6*√(4*1)=40-14.4=25.6

D(X+Y)=D(x)+ D(Y)+2ρxy(D(x) D(Y))^1/2D(X+Y)= D(x)+ D(Y)-2ρxy( D(x) D(Y))^1/2

D(X+Y)=DX+DY+2Cov(X,Y) =DX+DY+2(ρ√DX√DY) =9+16+2*(0.5*3*4) =9+16+12 =37

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