2.47 (a) Show that the m.g.f of a Poisson r.v. X with parameter A is Vx (!) = exp(2(e' - 1)). Find the mean and variance of X from its m.g.f. (b) Show that if the X, are independent Pois(); ) r.v.'s for / = 1. 2. ....n, then their sum is also Poisson distributed with parameter _2