Question: The random variables X and Y have joint density function f (x, y) = 12xy(1 x) 0 < x < 1, 0 < y

The random variables X and Y have joint density function
f (x, y) = 12xy(1 − x) 0 < x < 1, 0 < y < 1
and equal to 0 otherwise.
(a) Are X and Y independent?
(b) Find E[X].
(c) Find E[Y].
(d) Find Var(X).
(e) Find Var(Y).

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