Three students arrive at the beginning of office hours. The amount of time each of them stays is exponentially distributed with means 1, 1/2, and 1/3 hour.

(a) What is the expected time until only one student remains?
(b) Number the student's according to their exponential rates. Find the distribution of L= the departure rate for last student left.
(c) What is the expected time until all three students are gone?