For the infinite server queue with Poisson arrivals and general service distribution G, find the probability that

(a) the first customer to arrive is also the first to depart.

Let S(t) equal the sum of the remaining service times of all customers in the system at time t.

(b) Argue that S(t) is a compound Poisson random variable.

(c) Find E[S(t)].

(d) Find Var(S(t)).