1. Let Y1 , .... Y. ~ Uniform (0, 0). (a) First identify the minimum variance unbiased estimator for 0. No work need be shown: the MVUE was derived in class, and you may simply write it down here. Then compute the variance of the MVUE for 0. (b) Now determine the value of the following expression: TL E log fy (Y,10) Note : This may remind you of something you have seen in class, but watch out: there will be a catch ... (c) Someone tells you : I can compute the CRIB for unbiased estimators of 0 based on this expression! Explain, using your answer in part (a), why this is not true. This is a case where we run into one of the regularity conditions for computations related to the Fisher information and the CRLB, which we often sweep under the rug in class, since they hold for most distributions. For the uniform distribution, however, we run into one of them: here, we cannot exchange integration and derivation, as we did on p.4 of Notes 03. That is, Note : In general , if the range of a pdf depends on the parameter , then the CRLB theorem is not applicable (a) The MVUE is 7 + 1 n +1 IIIAX Fi - Y(m) [Note: Students don't need to show any work here. Just an answer is enough.] The cdf of V(m) is P(Y(m) Sy) = Therefore, the pdf of Y(m) is PYmm) (3) = dy " P ( Y ()