[20 points] Suppose that the signal X ~N(μ₁, σ) is transmitted over a communication channel. Assume that the received signal is given by Y = X +W, where W~N(µ2, σ½) is independent of X. (a) Find the MMSE estimate of X, given Y = y is observed. (b) Find the ML estimate of X, given Y (c) Find the MAP estimate of X, given Y y is observed. =y is observed.