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Three continuous random variables X, Y and Z have a joint density function JK, if x, y, z e [-1, 1] and ryz > 0;

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Three continuous random variables X, Y and Z have a joint density function JK, if x, y, z e [-1, 1] and ryz > 0; fxYz(I, y, z) = 0. otherwise; where K is a constant. (a) Find K. (b) Find fx(x), fv(y), fz(2) and fxy(r,y). Are X and Y independent? Are X, Y and Z independent? (c) Find fx(x | Y = ;) and fz(= [ X = 1, Y = ;). (d) Find the density function of W = XYZ

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