1. Suppose that the random variables X and Y are independent and N (0, σ2)- distributed.
(a) Show that X/Y ∈ C(0, 1).
(b) Show that X + Y and X - Y are independent.
(c) Determine the distribution of (X - Y )/(X + Y ).
2. Suppose that the moment generating function of (X, Y )t is ψX,Y (t, u) = exp{2t + 3u + t2 + atu + 2u2}. Determine a so that X + 2Y and 2X - Y become independent.