(i) If X1,...,Xn are i.i.d. with c.d.f. F and empirical distribution Fn, use Theorem 11.2.18 to show...

(i) If X1,...,Xn are i.i.d. with c.d.f. F and empirical distribution Fˆn, use Theorem 11.2.18 to show that n1/2 sup |Fˆn(t) − F(t)| is a tight sequence.

(ii) Let Fn be any sequence of distributions, and let Fˆn be the empirical distribution based on a sample of size n from Fn. Show that n1/2 sup |Fˆn(t)−Fn(t)|

is a tight sequence.