ELEC2844: PROBABILISTIC SYSTEMS ANALYSIS HOMEWORK 3 Question 10 In this question we explore the application of MAP and LMS estimation in a communication channel. Suppose we want to send a signal X, but this is corrupted by additive noise N such that the signal at the receiver is Y, where Y = X + N. We assume the noise is Gaussian with zero mean and a known variance, i.e., N ~N[0,02). We further assume that X is a continuous random variable with half of the probability clustered at +1 and half of the probability clustered at 1. (We say this, instead of calling X a discrete random variable, is so that the estimate does not necessarily have to be i]. We can formalize it in more rigorous mathematics using a delta function, but that is beyond the scope of this class.) 1. Find the MAP estimate of X. 2. Find the LMS estimate of X