5. If the moment-generating function of X is given by M(t) = 500t+1250t, where -co

5. If the moment-generating function of X is given by 500t+1250t2 where oo < x < 00, find P[6765 (X 500)2 12560]. 4 6. The pdf of Y is g(y) = i, where 0 < y < 00. (a) Calculate the value of c so that g(y) is a pdf. (b) Find E(Y) (c) Show that the Var(Y) is not finite. 7. If X has a gamma distribution with O 2, find < 5) 4, and a