Let X=U+W with E[U]=m, var(U)=v, E[W]=0, and var(W)=h. Assume that U and W are independent.

Question

The LLMS estimator of U based on X is of the form U^=a+bX. Find a and b. Express your answers in terms of m, v, and h using standard notation.

a=- unanswered
b=- unanswered
Suppose we further assume that U and W are normal random variables and then construct U^LMS, the LMS estimator of U based on X, under this additional assumption. Would U^LMS be the identical to U^, the LLMS estimator developed without the additional normality assumption in part (1)?

Yes - answered

Answer 1

Can someone please answer?

Answer 2

a=m*h/(v+h)
b=v/(v+h)

Answer 3

a=v/(v+h)
b=m*h/(v+h)
Yes