6. Additive noise channel with path gains (12 points). Consider the additive noise channel shown in Figurel]. The signal X and the noise Z have zero mean, variances P and N , respectively, and are uncorrelated, and a 5% 0 and 1) 7E 0 are constants. Find the linear MMSE estimate of X given Y and its MSE in terms only of P, N , a, and b. Z X E )& E >Y=b(aX+Z) Figure 1: Additive noise channel with path gains