The weather in Boston is either good, indifferent, or bad on any given day. If the weather is good today, there is a 60% chance the weather will be good tomorrow, a 30% chance the weather will be indifferent, and a 10% chance the weather will be bad. If the weather is indifferent today, it will be good tomorrow with probability 0.40 and indifferent with probability 0.30. Finally, if the weather is bad today it will be good tomorrow with probability 0.40 and indifferent with probability 0.50.

(a) What is the stochastic matrix for this situation? Order the weather types (good, indifferent, bad).

(b) Suppose there is a 50% chance of good weather today and a 50% chance of indifferent weather. What are the chances of bad weather tomorrow?

(c) Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the chances for good weather on Thursday?