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4. (25%) Consider random variables X and Y with joint density function c, 0 < x, 0 < y, x + y <1 (a)

4. (25%) Consider random variables X and Y with joint density function c, 0 < x, 0 < y, x + y <1 (a) Find c. f(x, y) = 0, elsewhere. (b) Find P(X - Y > 0). (c) Find the marginal density of Y. (d) Find the conditional density function fxy (xy). (e) Are X and Y statistically independent? Support your answer.

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