Suppose there are two tellers taking customers in a bank. service times at a teller are independent, exponentially distributed random variables, but the first teller has a mean service time of 2 minutes while the second teller has a mean of 5 minutes. there is a single queue for customers awaiting service. suppose at noon, 3 customers enter the system. customer a goes to the first teller, b to the second teller, and c queues. to standardize the answers, let us assume that ta is the length of time in minutes starting from noon until customer a departs, and similarly define tb and tc.(a) what is the probability that customer a will still be in service at time 12: 05? (b) what is the expected length of time that a is in the system? (c) what is the expected length of time that a is in the system if a is still in the system at 12: 05? (d) how likely is a to finish before b? (e) what is the mean time from noon until a customer leaves the bank? (f) what is the average time until c starts serv (g) what is the average time that c is in the system? (h) what is the average time until the system is empty? (i) what is the probability that c leaves before a given that b leaves before a? (j) what are the probabilities that a leaves last, b leaves last, and c leaves last? (k) suppose d enters the system at 12: 10 and a, b, and c are still there. let wd be the time that d spends in the system. what is the mean time that d is in the system?