1. (Estimation vs. Detection) Let X = 1 with probability -1 with probability ?, and the noise Z ~ Unif (-2, 2) be independent random variables. Their sum Y = X + Z is observed. (a) Find the conditional pmf pxy (x | y). Find the MMSE of X given Y and its MSE. (b) Suppose we use a decoder to decide whether X = 1 or -1. Using the pmf pxy(x | y) found in part (a), find the MAP decoder and its probability of error. Compare the MAP decoder's MSE to the minimum MSE