Question

Problem 9. Let Xi,..., Xn be a random sample from the distribution function F. Set rt j-1 a.s (1) Show that Fn (t) ^* F(t) for each t eR (2) Show that n/2(Fm(t) Ft)) »,z~(0, F) Ft)) for each t for which F(( F(t) is positive.

Answer 1

Part(a)

To Proof:

Hence, $F_n(t)\overset{a.s.}{\rightarrow}F(t) \ for \ all \ t\in \mathbb{R}$ Proved.

Part(b)

Proved