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How to calculate the mathematical expectation?
D(XY) = E{[XY-E(XY)]^2} ( 1)

= 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).