Let X denote the diameter of an armored electric cable and Y, the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density f(x, y) = 1/y, when 0 < x < y < 1, and 0, elsewhere. Find P (X + Y > 2/3) and find (a) the marginal distribution of X; (b) the marginal distribution of Y.

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Let X denote the diameter of an armored electric cable and Y, the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density f(x, y) = 1/y, when 0 < x < y < 1, and 0, elsewhere. Find P (X + Y > 2/3) and find (a) the marginal distribution of X; (b) the marginal distribution of Y.

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