Chicago has been struck by a crime wave. Alarmed by the increasing number of bank robberies and concerned about their effect on bank customers, the Banking Upper Management Society (BUMS) adopts the following policies at each bank:

one teller's window is reserved for the exclusive use of bank robbers.

in order to conserve space, bank robberies may be committed only by a lone bandit.

if two or more robberies occur simultaneously, the robbers are served on a first-come, first-serve basis.

You are engaged as a consultant by the Bank Robbers Federation (BARF). Your job is to determine if the proposed arrangement with the BUMS is adequate. The data you are given is: Robbers arrive at random 24/7 (during open hours), the average arrival rate is 2 robberies per hour. Teller service is exponential with an average of 10 min (special robber withdrawal forms expedite service)

You are asked to determine

(a) the probability that there is no robber in the bank (large t probability).

(b) the probability that the robber's teller is busy.

(c) the average number of robbers in the bank.

(d) the probability that a bank is hit at least 4 times by robberies during one hour.

(e) the probability that there is no robbery during a whole day.

(f) the probability that the time until the fifth robbery exceeds two days.