Question: 4. Let X = U + W with E[U] = m, var(U) = 1), E[W] = U, and var(W) = h. Assume that U and

 4. Let X = U + W with E[U] = m,

4. Let X = U + W with E[U] = m, var(U) = 1), E[W] = U, and var(W) = h. Assume that U and W are independent. (a) The LLMS estimator of U based on X is of the form fl = a. + bX. Find a and 15. Express your answers in terms of m, 111 and h. (b) Suppose we further assume that U and W are normal random variables and then construct 0333,131 the LMS estimator of U based on X under this additional assump- tion. Would U L MS he the identical to U, the LLMS estimator developed without the additional normality assumption 1n part (a)

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