On any day, independent of other days, the number of calls that a call center receives is Poisson distributed with
rate parameter \lambda = 2500. Currently, the call center has a maximum capacity of processing 2530 calls per day.
(a) (4p) On what percentage of days the call center will be able to respond all calls?
(b) (8p) Calculate the maximal rate parameter \lambda
∗
for which the call center will be able to respond all calls with
at least 0.95 probability with the current capacity?
(c) (8p) Suppose that the call center can process all calls that it gets and each call returns the call center a
random profit that is continuously and uniformly distributed between $0.20 and $0.50, independent of other
calls. Calculate the expected value and the variance for daily profit.