Let (x,y) have pdf f(x,y) = 1 over the region R = triangle with vertices (0,0), (1,0), (0,2) and f(x,y) = 0 elsewhere. Define Z = 2X + Y, W = 2X. a) Inverse transformation from (z,w) to (x,y) b) Jacobian J = c) sketch the region R in (x,y) coordinates d) sketch the region D in (z,w) coordinates e) Joint pdf over D, g(z,w) = f) Find pdf h(z) of Z from marginal of g(z,w) and sketch the graph H1

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