Question: Let X and Y have joint density f(x, y) = 12x(1 x), for 0 < x < y < 1. (a) Find the marginal

Let X and Y have joint density
f(x, y) = 12x(1 − x), for 0 < x < y < 1.
(a) Find the marginal densities of X and Y.
(b) Find the conditional density of Y given X = x. Describe the conditional distribution.
(c) Find P(X < 1/4|Y = 0.5)

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