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Suppose that three random variables X1, X2, and X3 have

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Suppose that three random variables X1, X2, and X3 have a continuous joint distribution for which the joint p.d.f. is as

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Suppose that three random variables X1, X2, and X3 have a continuous joint distribution for which the joint p.d.f. is as follows: f (x1, x2, x3) =  8x1x2x3 for 0 < xi < 1 (i = 1, 2, 3), 0 otherwise. Suppose also that Y1 = X1, Y2 = X1X2, and Y3 = X1X2X3. Find the joint p.d.f. of Y1, Y2, and Y3.

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