Consider the abstraction of a point-to-point wireless communication system. The trans- mitted signal X is an N(0, o2) random variable. The channel output is HX, and the receiver input is: Y = HX + V, where V is an N(0, 2) random variable that is independent of X and represents thermal noise in the amplifier circuitry. Suppose the channel is subject to in- termittent failure, e.g., due to fading. For simplicity, suppose H is a random variable taking the values 0 and 1 with probabilities (1 - p) and p, respectively. Assume H is independent of both X and V. . 4 POINTS Find the linear least squares estimate (LLSE) or conditional mean of X based on the observation Y: E[X|Y] = /cond, the variance of the LLSE, VAR[/cond], and the mean-square estimation error (MSE) or conditional variance:, cond. . 4 POINTS Show that EX |Y = y] = C. P(H = i|Y = y) E[X|Y = y, H = i]