= E{X? y? -2XYE(XY)+E? (XY)}
= E(X? )E(Y? )-2E? (X)E? (Y)+E? (X)E? (Y)
= E(X? )E(Y? )-E? (X)E? (Y) (2)
If E(X) = E(Y) = 0,
So D(XY) = E(X? )E(Y? )= D(X)D(Y),(3)
That is, when X and Y are independent of each other and their mathematical expectations are all zero, the variance d (XY) of the product xy of X and Y is equal to:
D(XY) = D(X)D(Y)。 (4) //: That is the formula (3).