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The joint probability density function (pdf) describing proportions X and Y of two components in a...

The joint probability density function (pdf) describing proportions X and Y of two components in a chemical blend are given by f(x, y) = 2, 0 < y < x ≤ 1.

(a) Find the marginal pdfs of X and Y.

(b) Find the probability that the combined proportion of these two components is less than 0.5.

(c) Find the conditional probability density function of Y given X = x. (d) Find E(Y | X = 0.8).

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