Please see the problem in the attachment.

6. MMSE and LMMSE [10 points, 10 points] Let Y = X +N , where X has the exponential distribution with parameter A and N is Gaussian with mean 0 and variance 02. The variables X and N are independent, and the parameters A and 02 are strictly positive. Find E [X |Y] (the LMMSE estimator) and the mean square error for estimating X using E[X |Y]