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.
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
No, I have a less biased estimator for µ than were given in the problem (the two µ above) and the one I created which is µ=(X1+X2+X3)/3. Unbiased and less variance than the other two equations. I think my problem is that it confuses me that the equation is made up of a mean and a variance and not of variables, I don't know whether I should just treat those as variables or if there's some weird estimator thing that wasn't covered in my lecture/in the books.
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