# Math Help - Unbiased Estimator

1. ## Unbiased Estimator

X1,...Xn~N(mu,sigma^2)
(sigma^2 known)

is the estimator mu=(average(x))^2-((sigma^2)/n)
an unbiased estimator to mu^2 ?

cheers

2. yes, since sigma is known
AND normality has nothing to do with this

3. why is it unbiased, how did you work it out ?

4. $E(\bar X^2) =V(\bar X) + (E\bar X)^2={\sigma^2\over n}+\mu^2$

5. just one question if I might:

an estimator T is unbiased if E(T)=parameter

where in the solution we calculated E(T) ?