Help with unbiased estimators

akerkhoff

New Member
I'm working on a homework problem and the question I'm stuck on is as follows:

"Give an unbiased estimator for 2µ+3σ^2"

I'm not sure how I would go about doing that since the mean and the variance make up the function.

Dason

Do you know an unbiased estimator for $$\mu$$? What about for $$\sigma^2$$?

akerkhoff

New Member
What I have is the following two unbiased estimators for µ, µ1: (X1+2X2+3X3)/6 and µ2: (X1+4X2+X3)/6. I've already calculated their bias (none) and their variance. I've also created an unbiased estimator with less variance than those two. Now all that's left is to give an unbiased estimator for 2µ+3σ^2

Dason

Do you know an unbiased estimator for $$\sigma^2$$?