Peter runs a small business classifying each day as good, moderate, or bad. The transition process is Markov with transition matrix (1.2.2). A daily income is a r.v. assuming values 1 or 2 on a bad day; 2 or 3 on a moderate day; and 3 or 4 on a good day; in all these three cases, with equal probabilities. Find

(a) The expected daily income in the long run;

(b) The probability that, in the stationary regime, the income on a particular day will exceed two units.