The gate at a public parking lot requires maintenance or replacement from time to time. Each week, there is a probability p that a car will crash into the gate, in which case it will be replaced at the beginning of the following week. If there is no accident for five weeks, the gate will always be replaced at the beginning of the following week. Let Xt denote the age of the gate at the beginning of week t . Is the long-run state probability vector of this Markov chain stationary? If so, find the long-run stationary probabilities.