5. (a) A certain machine often breaks down and needs to be fixed. At time 0, the machine is working. It works for an Expo() period of time (measured in days), and then breaks down. It then takes an Expo()) amount of time to get it fixed, after which it will work for an Expo(A) time until it breaks down again, after which it will take an Expo()) time to get it fixed, etc. Assume that these Expo(X) r.v.s are i.i.d. A transition occurs when the machine switches from working to being broken, or switches from being broken to working. Find the distribution of the number of transitions that occur in the time interval (0, t). (Simplify.)