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I currently know: $$Var(XY)=E(X^2Y^2)−[E(XY)]^2$$ $$=E(X^2)E(Y^2)−[E(X)]^2[E(Y)]^2$$ but I am lost where to go from there. I can vaguely see the the formula $Var(X)=E(X^2)-E(X)^2$ hidden somewhere, but I do not know how variance out of the equation.

Thanks!

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  • $\begingroup$ Solve for $E(X^2)$ in the equation for $Var(X)$ and plug this into your last line. $\endgroup$ – Breaking Waves Oct 10 '20 at 19:43