UV=acXY+adX+bcY+bd
E(UV)=acE(XY)+adEX+bcEY+bd
EU=aEX+b
EV=cEY+d
EU*EV=acEXEY+adEX+bcEY+bd
因此两式相减得
E(UV)=EU*EV
=ac[E(XY)-EXEY]
=ac Cov(XY)
UV=acXY+adX+bcY+bd
E(UV)=acE(XY)+adEX+bcEY+bd
EU=aEX+b
EV=cEY+d
EU*EV=acEXEY+adEX+bcEY+bd
因此两式相减得
E(UV)=EU*EV
=ac[E(XY)-EXEY]
=ac Cov(XY)