# Define $Var(XY)$ in terms of $E(X)$, $E(Y)$, $Var(X)$, $Var(Y)$ for Independent Random Variables $X$ and $Y$ [duplicate]

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!

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