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Suppose that the joint distribution of X and Y is uniform over a set A in the xy-plane. For which of the following sets A are X and Y independent? (a) A circle with a radius of 1 and with its center at the origin. (b) A circle with a radius of 1 and with its center at tbe point (3,5). (c) A square with vertices at the four points (1, 1), (I, - I), (-1, - I), and (-1, 1). (d) A rectangle with vertices at the four points (0, 0), (0,3), (1, 3), and (1, 0). (e) A square with vertices at the four points (0, 0), (1, 1), (0, 2), and ( - 1, 1).

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