please provide all steps and explain which theorems you are applying.: answers are provided

Let X = U + W with E [U] = m, Var (U) = v, E [W] = 0, and Var (W) = h. Assume that U and Ware independent. 1. The LLMS estimator of U based on X is of the form U = aX + b. Find a and b. Express your answers in terms of m, U, and h using standard notation. a = v/(vth) uth b = m*h/(v+h) m.h uth 2. We now further assume that U and are normal random variables and then construct LMS, the LMS estimator of U based on X, under this additional assumption. Would U LMS be identical to U, the LLMS estimator developed without the additional normality assumption in Part 1? Yes