The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 60% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 10% chance it will be bad. If the weather is indifferent today, there is a 70% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 3030% chance it will be good tomorrow and a 30% chance it will be indifferent.
(a) What is the stochastic matrix for this situation?
(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 60% indifferent and 40% bad weather. What are the chances for good weather on Wednesday?