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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?

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

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I'll start you with a hint to give you chance to finish it yourself (and because I'm on my phone)

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

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  • $\begingroup$ Thanks, thats more than enough :) i think i tried from bottoms up approach. $\endgroup$ – octarine Sep 22 '16 at 17:03

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