A total of n people has been invited to a party honoring an important scholar. The party begins at time 0. The arrival time of the n guests are...

A total of n people has been invited to a party honoring an important scholar. The party begins at time 0. The arrival time of the n guests are independent exponential r.v.s with mean 1, and the arrival time of the scholar is uniformly distributed between 0 and 1.

(a) Find the probability that exactly k of the guests arrive before the scholar.

(b) Find the expected number of guests who arrive before the scholar.