1. Show that as the estimator of Prob. 3 becomes efficient. Hint: note that the estimate is Gaussian with mean A and variance known results for the moments of a Gaussian RV.
Use the CRLB for transformed parameters (see App. A) and Eq. (7.15) to determine the CRLB for the signal power A2. Additive WGN, it seems plausible that an efficient estimator for A2 might be the square of the sample mean Show that this estimator is not efficient even though the estimator for was efficient. Hint: consider the estimator bias.
2. Determine whether an alternative power estimator for the real-valued constant-in-AWGN problem that forms the sample mean of 2, is efficient. If not, is it asymptotically efficient?