Please help with these problems. Thanks

A device parameter X is a continuous random variable that takes values over [ 2 ,2] and is uniform over that interval. We take a measurement Y pX + N where p 72 0 is a given parameter and N~ ~N(0, a 2) is independent noise. Dene X1 (Y) aY as the linear MMSE estimator (for an optimized {1). Dene X2(Y)= [X1(1/))]E2. Dene X3(Y) = ]E[X|Y]. Assume p 0 7. a) Compute the optimal a and the corresponding MSE for estimator X1(Y). b) Compute X3(y) 2 IE [X |Y = y] for all y E R. It will be an integral divided by another integral (if you want, you can compute the numerator in closed form and you can compute the denominator in terms of the Q() function if you want). c) Write a program that for values 02 E [0. 01 ,20] does the following: Given a2 run 73 10000 samples to 2generate i.i. d. (X,,Y) values. Take the empirical values MSElemmg-caz 1,12% 1(X1 (Y) X ,)2. Plot as a function of a2 and compare with the theoretical value for MSE in part (a), also compare with the constant Var-(X) which is the MSE obtained by the best constant estimator. d) In the same graph, compare MSE2gmpmmg = Z:=1(X2(Y,-) X02. Explain your observations ]