Assignment:
Consider a machinery that cycles along three different states, namely (1) working, (2) broken, (3) under repair. Suppose that, when the machine is working, hazards occur according to a Poisson process with parameter λ. Furthermore, assume that the machinery remains in broken state for an exponential random time with parameter µ and that the repair takes an independent random time with exponential distribution with parameter ζ. Compute the asymptotic probability of the working state.