Question: 12. For # = $ (x, y): 0 < x + y < 1, 0 < x < 1, 0 < y < 1 %

12. For # = $ (x, y): 0 < x + y < 1, 0 < x < 1, 0 < y < 1 % , a region in the plane, let f (x, y) = B 3(x + y) if (x, y) ∈ # 0 otherwise be the joint probability density function of the random variables X and Y . Find the marginal probability density functions of X and Y , and P (X + Y > 1/2).

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