If X1,... Xn constitutes a random sample from a population with mean u what condition must be imposed on the constraints a1,...an so that

u^ = a1X1 + ...+ anXn

If o^ is an unbiased estimator for o what condition must be imposed so that o^2 is an unbiased estimator for o^2? Does this seem like a reasonable condition to impose? Why?

I'm struggling to understand the concept of this question. Any help or explanation will be appreciated.