2.32 Let Mx(t) be the moment generating function of X, and define S(t) = log(Mx (t)). Show that d 2 = EX and = Var X. dt S(t) dt2 S(t) 1=0 1=0 2.33 In each of the following cases verify the expression given for the moment generating function, and in each case use the mef to calculate E X and Var X