The weather can be considered a stochastic system, because it evolves in a probabilistic manner from one day to the next. Suppose for a certain location that this probabilistic evolution satisfies the following description: There are two possible kinds of weather: rain or sunshine. The probability of rain tomorrow is 0.5 if it is raining today and 0.1 if today is sunshine. The probability of its being sunshine tomorrow is 0.9 if it is sunshine today and 0.5 if is raining today. This is repeated for the following days (i.e., the weather of day i+ 1 depends on the weather of day i). Please do the following:

1. Elaborate an Excel simulation model for the weather for the following 15 weeks (105 days) and report the weekly average of rainy days if today (day 0) is raining (40 points).

2. Now define the weather for the following 15 weeks (105 days) and report the weekly average of rainy days if today (day 0) is clear (40 points).

3. Compute the 95% confidence intervals for both cases and indicate if there is any difference if today (day 0) is raining or not, with a maximum halfwidth of 0.5 days (20 points).