Question: Let X and Y be two independent identically distributed random variables with the uniform probability density (u) = 1 for 0 ≤ u ≤ 1. Let Z = X + Y .
(a) Find XˆLLS(Z) and KLLS, the linear least-squares estimate of X based on the observation Z, and its mean-square error variance.
(b) Find XˆMSE(Z) and KMSE, the least-squares estimate of X based on the observation Z, and its mean-square error variance.