(i) If X1,..., Xn are i.i.d. with c.d.f. F and empirical distribution F n, use Theorem 11.4.3...

(i) If X1,..., Xn are i.i.d. with c.d.f. F and empirical distribution Fˆ

n, use Theorem 11.4.3 to show that n1/2 sup |Fˆ

n(t) − F(t)| is a tight sequence.

(ii) Let Fn be any sequence of distributions, and let Fˆ

n be the empirical distribution based on a sample of size n from Fn. Show that n1/2 sup |Fˆ

n(t) − Fn(t)| is a tight sequence.