2.  (6 points total) This problem is similar to Problem 2 in…

2.  (6 points total) This problem is similar to Problem 2 in HW6. The weather for each day can be classified as being either rainy (state 0), cloudy (state 1), or sunny (state 2). If it is currently raining, then the probabilities for the weather condition to be rainy, cloudy, and sunny next day will be 4/8, 3/8, and 1/8, respectively. If the current day is cloudy, then the probabilities for the weather condition to be rainy, cloudy, and sunny next day will be 3/8, 2/8, and 3/8, respectively. If the current day is sunny, then the probabilities for the weather condition to be rainy, cloudy, and sunny next day will be 1/8, 3/8, and 4/8, respectively.        (a)  (3 points) Draw the three-state probability diagram.        (b)  (3 points) What are the respective percentages of rainy, cloudy, and sunny days in the long run?