6. Consider two random variables X and Y with the joint probability density f(x, y) =...

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6. Consider two random variables X and Y with the joint probability density f(x, y) = { 12xy(1 – y), 0<x < 1,0 < y < 1 elsewhere. Let Z = XY2 and W = Y be a joint transformation of (X,Y). (a) Sketch the graph of the support of (Z, W) and describe it mathematically. 6. Consider two random variables X and Y with the joint probability density f(x, y) = { 12xy(1 – y), 0<x < 1,0 < y < 1 elsewhere. Let Z = XY2 and W = Y be a joint transformation of (X,Y). (a) Sketch the graph of the support of (Z, W) and describe it mathematically.