Let X and Y have the joint density function f (x, y) = k(x ? y), for 0 ? y ? x ? 1, and 0 elsewhere.
(a) Draw the region over which the density is positive and employ it in determining limits of integration to answer the next questions.
(b) Find k.
(c) Find the marginal densities of X and Y.
(d) Find the conditional densities of Y given X and X given Y.