Recall our simplified version of Babylonian solar motion: e fast zone - 30 per month; e slow zone - 287'30\" per month. For simplicity, say the fast zone is 0-180 and the slow zone is 180-360. Exercise 1. Suppose that today the Sun is at 360 = 0. Where will it be 450 days from now? Exercise 2. Show that this system does not lead to a 365 day year. Determine how big the fast and slow zones should be so that the year is 365 days long. Problem 3. Assume that f(z;0) =e % z >0, R. Confirm that X () is the MLE of and X1y (1) is an unbiased estimator of with variance 1 Is X1y (1) an MVUE of 67