(Properties of the empirical distribution) Let X1,...,Xn be an i.i.d sample from a distribution function F. The empirical distribution function Fn(t) is defined as Fn(t) = 1/n sum from i=1 to n I(Xi <= t), where I(·) is the indicator function. Assume t is any fixed constant. (a) Show that Fn(t) is an unbiased estimator of F(t). (b) Derive the distribution of Fn(t). (c) For any fixed t, as n -> infinity show that sqrt(n)(Fn(t) - F(t)) ->d N(0, v(t)), and determine the value of v(t). Here ->d means convergence in distribution.