Question: Let ( X , Y ) be a uniformly distributed random point on the quadrilateral D with vertices (0, 0), (2, 0), (1, 1) and

Let (X, Y) be a uniformly distributed random point on the quadrilateral D with vertices (0, 0), (2, 0), (1, 1) and (0, 1).

(a) Find the joint density function of (X, Y) and the marginal density functions of X and Y.

(b) Find E[X] and E[Y].

(c) Are X and Y independent?

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