Please see the problem in the attachment.

Recall that for two independent random variables X and Y with PDFs fx and fy, respec- tively, the joint PDF of X and Z, where Z = X + Y, is given by fxz(x, z) = fx(x) fy (2 -x). Consider two independent exponential random variables X1 and X2 with parameter 1. Let Y1 = X1, Y2 = X1 + X2. Find the MMSE estimate of Y1 using Y2