Each entering customer 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 server i is an exponential random variable with rate $\backslash$mu i $,$ i $=1,2,3.$ Suppose you enter the system when it contains a single customer who is being served by server $3.(10$ p$)$ Find the probability that server $3$ will still be busy when you move over to server $2.(10$ p$)$ Find the probability that server $3$ will still be busy when you move over to server $3.(15$ p$)$ Find the expected amount of time that you spend in the system. $($Whenever you encounter a busy server, you must wait for the service in progress to end before you can enter service.$)(15$ p$)$ Suppose that you enter the system when it contains a single customer who is being served by server $2.$ Find the expected amount of time that you spend in the system.