37. Consider an infinite server queueing system in which customers arrive in accordance with a Poisson process and where the service distribution is exponential with rate ì. Let X(t) denote the number of customers in the system at time t. Find

(a) E[X(t + s)\X(s) = n]

(b) Vai[X(t + s) \X(s) = n]

Hint: Divide the customers in the system at time t + s into two groups, one consisting of "old" customers and the other of "new" customers.