2. Suppose that X1, ..., Xn are independent identically distributed random variables with E(X1) = / and V(X1) = 02. Let Xodd be the sum of the X; with odd numbered indices divided by the number of odd indices and let Xeven be the sum of the X, with even numbered indices divided by the number of even indices. (a) Show that both Xodd and Xeven are unbiased estimators of /. (b) Out of these two estimators, which would you pick based on the MVUE principle? Don't forget to justify your answer. 3. Suppose that To > 0 is fixed. Let X1, ..., Xn be independent identically distributed random variables with density f(x|0) = 0 Orex -0-1 for r > To otherwise (a) Write down the joint distribution function / likelihood function. (b) Write down the log-likelihood function. (c) Find the maximum likelihood estimate of 0