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Let X and Y be random variables such that 0 < ?2 X < ? and 0 < ?2 Y < ?. Suppose that U = aX + b and V = cY + d, where a

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Let X and Y be random variables such that 0 < ?2 X < ? and 0 < ?2 Y < ?. Suppose that U = aX + b and V = cY + d, where a = 0 and c = 0. Show that ?(U, V ) = ?(X, Y ) if ac > 0, and ?(U, V ) = ??(X, Y ) if ac < 0.

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