The weather in Rainesville is sunny, cloudy, or rainy. Suppose that tomorrow's weather depends only on today's weather. If it is sunny today, it will be cloudy tomorrow with probability 0.3 and rainy with probability 0.5. If it is cloudy today, it will be sunny tomorrow with probability 0.3 and rainy with probability 0.6. If it is rainy today, it is sunny tomorrow with probability 0.1 and cloudy with probability 0.2

If it is sunny today, what is the expected number of rainy days for the rest of the week (6 days ahead)? 3. (15 pts) If it is sunny today, what is the probability of having 3 consecutive rainy days for the rest of the week (6 days ahead)? 4. (15 pts) If it is rainy today, what is the expected number of days until a sunny day? 5. (15 pts) What is the long-run proportion of days without rain?