Question: 3. A point (X, Y) is selected at random inside a triangle defined by {(x, y) : 0 3. A point (X, Y) is selected

3. A point (X, Y) is selected at random inside a triangle defined by {(x, y) : 0

3. A point (X, Y) is selected at random inside a triangle defined by { (x, y) : O y a; < 1}. Assume the point is equally likely to fall anywhere in the triangle. (a) Find the joint cdf and joint pdf of X and Y. (b) Find the marginal cdf and marginal pdf of X and Y. (c) Find the probabilities of the following events in terms of the joint cdf: A = 1/2, Y 3/4}; B = {1/4 < X 3/4, 1/4 < Y 3/4}. (d) Find < X2).

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