After being repaired, a machine functions for an exponential timewith rate λ and then
fails. Upon failure, a repair process begins. The repair processproceeds sequentially
through k distinct phases. First a phase 1 repair must beperformed, then a phase 2,
and so on. The times to complete these phases are independent, withphase i taking
an exponential time with rate μi, i = 1; ; k.

(a) What proportion of time is the machine undergoing a phase irepair?
(b) What proportion of time is the machine working?