2. Let X be a Chi-squared random variable with density function a fx (x) = exp x > 0. Suppose Y is independent of, and has the same distribution as, X. (a) Let Z = vX. Show that the density function of Z is given by %3D fz(z) = 2a exp z > 0. Hence state the value of a. (b) Let V = X +Y and W = X/Y. Show that the joint density of V and W is given by 1 fv,w(v, w) = v, w > 0. ev/2 2T /w(w +1)

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