Please answer the following questions.

Problem 8.3 The random variables X , Y have joint probability density function mx+m OSmSysl 0 else fX,Y($Jy) = { (a) Find the MAP estimate of X given the observation Y = y. (b) Let 6 = X {EMAP(Y). Find E[2], the mean square error of the MAP estimate. (0) Find the minimum mean square error estimate of X given the observation Y = y. (d) Find the linear least square error estimate of X given the observation Y = y. (Hint: think before you start computing...) (e) Find the expected value of the square of the error, E[(X LELLSE(Y))2]