8. Two patients regularly need the same two-day treatment at a local hospital. That is, on a given day, each patient may or may not be needing treatment. If the patient does not need treatment, he does nothing. If a patient does need the treatment, he must make a request before the treatment can be carried out. The treatment starts immediately once a request is made. However, if the patient makes a request on a day where the other patient has already made a treatment request on the same day, or on a day where the other patient is currently in the treatment, then the patient making the new treatment request has to wait until the other patient finishes his own treatment. Assume that on a given day, the probability that a patient makes a request to have the treatment is p. (a) Can you model the evolution of two patients' conditions/states on the treatment us- ing a Markov Chain? If so, write down the states and the corresponding transition probability matrix. (b) Show if the stationary probabilities exist. If so, calculate the stationary probabilities. (c) What is the long-run proportion of time that neither patient needs the treatment