I don't understand what the question is asking. Any explanation is appreciated.

{15 points} Let X1, ...,X be a random sample from a normal distribution with mean n and variance of and H, ..., Y\" be a random sample from a normal distribution with mean a and variance 0%. Assume the two samples are independent. {a} Show that fr. = wX + {1 - w}Y is an unbiased estimator for n. (5 points) [b] For what value of a: is the varianee of f; minimized? {5 points) (1:) Let [11 be the estimator when w attains the value found in (h) and let g be the estimator when a: = 1,52. Find the relative elilieiennzzyr of [:1 to g. [5 points}