Each customer who enters a certain business must be served first by server 1, then by server 2, and finally by server 3. The amount of time it takes to be served by a server is an exponential random variable with a rate . Suppose you enter the sytem at a time when it contains a single customer who is being served by server 3.
a. What is the probability that server 3 will still be busy when you move over to server 2?
b. What is the probability that server 3 will still be busy when you move over to server 3?
c. Suppose that . Find the expected time that you spend in the system.
