Given that X and Y are normally distributed as N(0,3) and N(0,5) respectively, what is the expected value of (XY)^2? Given that X and Y are independent and normally distributed as N(0,3) and N(0,5) respectively, what is the expected value of (XY)^2?

The trick here is to rewrite the expected value in terms of several rules that you have learned in class. Maybe the following rules ring a bell:

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*$E[XY] = E[X]\cdot E[Y] \quad \text{if $X$ and $Y$ are independent}$

*$E[X^2] = \text{Var}[X]+ E[X]^2$
