# Expected value of Combined random variable with function E(X^2Y^3) [closed]

ok, so the question goes like this. see embedded link enter image description here

I have no problem finding E[X] and E[Y] using iterative expectation. Unfortunately, X and f(Y|X) is not independent therefore simply multiplying E[X] and E[Y] will not give the final outcome. Any suggestion on how to do this? or Must we use rigorous method of integration etc?

## closed as off-topic by Did, Claude Leibovici, Qwerty, tatan, PragabhavaSep 22 '16 at 19:34

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$$E[Y^2X^3] = E[E[Y^2X^3 | X]] = E[X^3E[Y^2 | X]]$$