7. Let the random variables in the sequence {Xn} be iid with a gamma density having parameters a ¼ 2 and b ¼ 3.

(a) What is the probability density for X n?

(b) What is the asymptotic probability density for X n?

(c) Plot the actual versus asymptotic probability density for X n when n ¼ 10.

(d) Repeat

(c) for n ¼ 40. Interpret the graphs in

(c) and (d)

in terms of asymptotic theory.