Problem 5 (More on MLE of a uniform distribution). Let X; be i.i.d uniform on [0,0]. Let n be the MLE for that you obtained from the previous exercise. a) Show that P[n -> ] = 0 for any > 0. b) For any > 0, determine an explicit expression for the probability c) Compute, for any > 0, the limit. P[| - 0| > ] P||Vn(n 0)| > as n . d) What do your previous answers suggest about the asymptotic distribution of Vin 0)? In particular, does this still look approximately normal? Does this violate our theorem on the asymp- totic normality of maximum likelihood estimates? Why or why not? 2 e) What is the Method-of-Moments estimate for 0, MOM? What is the limiting distribution of n(MOM-00) where 0 is the true value of the parameter?