PROBLEM 2 [25 Forms} MODELING (SQUID-19 Tasman: arr PURDUE Purdue Universityr Student Health {PUSH} has two machines for processing the weekly randomized tests. Machine 1 has a failure rate of 1 per month. while machine 2 has a failure rate of 115 per month. Assume that the time to failure is exponentially distributed. On the other hand. if machine 1 fails the time to repair takes on average 3 days, while for machine 2 the time to repair is 1 week, on atren age. Again. assume that the time to repair is exponentially distributed and suppose that there are. turn technicians assigned to repairing the machines. 1. Model the availability of the machines using a Mark-air chain. 2. 1ul'lihat is the probability that neither machine is available {both in the short-term. as Iwell as the long-run]? 3. On average. in the long-run. how many machines will be available each month? Solution