# Question

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).

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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