已知DX=25,DY=36,ρ=0.4,求D(X+Y),D(X-Y),D(2X+3Y)
问题描述:
已知DX=25,DY=36,ρ=0.4,求D(X+Y),D(X-Y),D(2X+3Y)
答
协方差COV(X,Y)=根号(DX)*根号(DY) *0.4=5*6*0.4=12D(X+Y)=DX+DY+2*COV(X,Y)=25+36+2*12=85D(X-Y)=Dx+Dy-2*COV(X,Y)=25+36-2*12=37协方差COV(2X,3Y)=2*3*COV(X,Y)=72D(2X+3Y)=4DX+9DY-2*COV(2X,3Y)=-440...