The weather in Edinburgh is either good, indifferent, or bad on any given day. If the weather is good today, there is a 50% chance the weather will be good tomorrow, a 30% chance the weather will be indifferent, and a 20% chance the weather will be bad. If the weather is indifferent today, it will be good tomorrow with probability .20 and indifferent with probability .70. Finally, if the weather is bad today, it will be good tomorrow with probability .10 and indifferent with probability .30.

a. What is the stochastic matrix for this situation?
b. Suppose there is a 30% chance of bad weather today and a 70% chance of indifferent weather. What are the chances of good weather tomorrow?
c. Suppose the predicted weather for Friday is 50% indifferent weather and 50% good weather. What are the chances for bad weather on Sunday?