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    Help with unbiased estimators




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

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

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

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    Re: Help with unbiased estimators

    Do you know an unbiased estimator for \mu? What about for \sigma^2?
    I don't have emotions and sometimes that makes me very sad.

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    Re: Help with unbiased estimators

    What I have is the following two unbiased estimators for , 1: (X1+2X2+3X3)/6 and 2: (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 2+3σ^2

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    Re: Help with unbiased estimators

    Do you know an unbiased estimator for \sigma^2?
    I don't have emotions and sometimes that makes me very sad.

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    Re: Help with unbiased estimators


    No, I have a less biased estimator for than were given in the problem (the two above) and the one I created which is =(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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