A discrete-time sequence s[n] is transmitted over a noisy channel and retrieved. The received sequence x[n] is modeled as x[n] = a [n] + w[n] where w[n] and a represents the channel noise and attenuation respectively. At a particular time instant n = n0, suppose x[n0], [n0] and w[n0] are random variables, which we denote as X, and W respectively. We assume that and W are independent, that W is distributed as a Gaussian N(0, 1) and the signal is distributed as a Gaussian N(10, 3). Please compute:

1. The LMS estimator of given X in function of a.

2. The Linear LMS estimator of given X. How are both estimators related?