Suppose that X and Y are random variables with joint PDF fX,Y (x, y) that is constant in the shaded area depicted in Figure P8.5, and zero elsewhere.
(a) Find the LMMSE estimator of Y based on measuring X.
(b) For x in the range -2 to 2, make a fully labeled sketch of the MMSE estimator of Y. How does the corresponding estimator compare with that in (a)?