Let X1, X2, . . . , Xn be a sequence of independent random variables, all having a common density function fX. Let A = Sn/n be their average. Find fA if
(a) fX(x) = (1/√2π) e−x2/2 (normal density).
(b) fX(x) = e−x (exponential density).
Hint: Write fA(x) in terms of fSn(x).