Let Xn denote the mean of a random sample of size n from a distribution that has p.d.f. f( x) = e-x, 0 <>x <>oo, zero elsewhere.
(a) Show that the m.g.f. M( t; n) of Yn = Jr,( in - I ) is equal to [e'1.J,, - (t/ Jr,)e1IJnJ -n, t Jn.
(b) Find the limiting distribution of Yn as n -+ oo.
This exercise and the immediately preceding one are special instances of an important theorem that will be proved in the next section.