Question

已知DX=25,DY=36,ρ=0.4,求D(X+Y),D(X-Y),D(2X+3Y)

Answer 1

协方差COV（X,Y）=根号(DX)*根号(DY) *0.4=5*6*0.4=12

D（X+Y）=DX+DY+2*COV（X,Y）=25+36+2*12=85

D（X-Y）=Dx+Dy-2*COV（X,Y）=25+36-2*12=37

协方差COV（2X,3Y）=2*3*COV(X,Y)=72

D(2X+3Y)=4DX+9DY-2*COV(2X,3Y)=-440

注:设C, a, b=Const, DCX=C^2DX , COV(aX,bY)=a*b*COV(X,Y)