Questions for (a)(i),(ii). Question very complicated. Please guide me with a full solution. Thanks

(a) The discrete random variable X has the following probability function, a, x =1, 2, 3, 5 f(x) = 1b, x=8 0, otherwise where a and b are constants. Given E[X] =5, find the values of a and b. ii.) Suppose M. (1) = =(e"+e-2 +1) + (e" + 3e' ). Given W = 2 X|, find the CDF of w, F(w)