1. Estimation us. detection. Let the signal X = +1, with probability 191-191- -1, with probability and the noise Z ~ Unif -2, 2 be independent random variables. Their sum Y = X + Z is observed. (a) Find the LMS estimate of X given Y (b) Find the (overall) MSE for the estimator you find in part (a). (c) Now suppose we use a decoder to decide whether X = +1 or X = -1 so that the probability of error is minimized. Find the MAP decoder and its probability of error. Compare the MAP decoder's MSE to the least MSE