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The joint probability density function of two random variables X and Y is f(x, y) =...

The joint probability density function of two random variables X and Y is f(x, y) = 4xy for 0 < x < 1, 0 < y < 1, and f(x, y) = 0 elsewhere.

(i) Find the marginal densities of X and Y .

(ii) Find the conditional density of X given Y = y.

(iii) Are X and Y independent random variables?

(iv) Find E[X], V (X) and covariance between X and Y .

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