Commercial fishermen in Alaska go into the Bering Sea to catch all they can of a particular species (salmon, herring, etc.) during a re-stricted season of a few weeks. The schools of fish move about in a way that is very diffcult to predict, so the fishing in a particular spot might be excellent one day and terrible the next. The day-to-day records of catch size were used to discover that the probability of a good shing day begin followed by another good day is 0.5, by a medium day is 0.3, and by a poor day is 0.2. A medium day is most likely to be followed by another medium day, with a probability of 0.6, and equally likely to be followed by a good or bad day. A bad day has a 0.3 probability of begin followed by a good day, 0.2 of begin followed by a medium day and 0.5 probability of begin followed by another bad day.

(a) Construct a Markov chain model to describe the way the fishing days run.

(That is, give the state space and the corresponding probability transition matrix.)