The joint density of X and Y is f(x, y) = xe 3xy , 1 < x

Question:

The joint density of X and Y is f(x, y) = xe^−3xy, 1 < x < 4, y >0.

(a) Describe the marginal distribution of X.
(b) Describe the conditional distribution of Y given X = x.
(c) Find E[Y|X].
(d) Use the law of total expectation to show E[Y] = ln4/9.
(e) Find E[XY] by conditioning on X.
(f) Find Cov(X, Y).

Distribution
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