An engineering professor purchases a new computer every two year with preferences for three models: MI, M2, and M3. If the present model is Ml, the next computer may be M2 with probability 0.2 or M3 with probability 0.15. If the present model is M2, the probabilities of switching to Ml and M3 are 0.6 and 0.25, respectively. And, if the present model is M3, then the probabilities of switching to Ml and M2 are 0.5 and 0.1, respectively. Represent the situation as a Markov chain and determine the probabilities that the professor will purchase the current model in 4 years, that is P{Mi|Mi}, where i=1,2,3. Remark: two-year period represents 1-step transition, so 4-year period represents 2-step transition.