Let F(t) be a cumulative distribution function and B°(u) a Brownian bridge. (a) Determine the covariance function for B°(F(t)). (b) Use the central limit principle for random functions to argue that...

Let F(t) be a cumulative distribution function and B°(u) a Brownian bridge.

(a) Determine the covariance function for B°(F(t)).

(b) Use the central limit principle for random functions to argue that the empirical distribution functions for random variables obeying F(t) might be approximated by the process in (a).