Editing Variance (section)

====Product of independent variables====

If two variables X and Y are [[Independence (probability theory)|independent]], the variance of their product is given by<ref>{{Cite journal |last=Goodman |first=Leo A. |author-link=Leo Goodman |date=December 1960 |title=On the Exact Variance of Products |journal=Journal of the American Statistical Association |volume=55 |issue=292 |pages=708–713 |doi=10.2307/2281592 |jstor=2281592}}</ref>
<math display="block">\operatorname{Var}(XY) = [\operatorname{E}(X)]^2 \operatorname{Var}(Y) + [\operatorname{E}(Y)]^2 \operatorname{Var}(X) + \operatorname{Var}(X)\operatorname{Var}(Y).</math>

Equivalently, using the basic properties of expectation, it is given by

<math display="block">\operatorname{Var}(XY) = \operatorname{E}\left(X^2\right) \operatorname{E}\left(Y^2\right) - [\operatorname{E}(X)]^2 [\operatorname{E}(Y)]^2.</math>