The random variables X and Y have joint density p(x, y) = 12xy(1 − x),         0 < x < 1,         0 < y < 1, and equal to 0 otherwise. (a) Are X and Y indepe

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The random variables X and Y have joint density

p(x, y) = 12xy(1 − x),         0 < x < 1,         0 < y < 1,

and equal to 0 otherwise.

(a) Are X and Y independent?
(b) Find EY .
(c) Find Var(X).
(d) Find the density of X + Y .

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