# Distribution of the statistic?

• yhp266

#### yhp266

Hi all, I've been confused about this for a while. Since it wasn't mentioned in class or my textbook, it probably reflects a fundamental lack of understanding :(

With any unbiased estimator, why is the distribution of the estimates also the distribution of the statistic?

Eg, suppose we have 5 independent and identically distributed normal random variables with variance 1 and mean (unknown parameter).

We observe some numbers say { 4, 5, -2 ,7 , 12}.

and we use sample mean as the estimator for mean. The sample mean is clearly normally distributed.

But why is this also the distribution for mean

And is it possible to have 2 different unbiased estimators for the same parameter?

Wouldnt it not make sense to have multiple distributions of estimates for a particular parameter

Last edited:
1/I don't understand your first question.
2/Yes, many unbiased estimators for one parameter is possible. Let x1,x2,...,xn be a sample form N(mu,sigma). Then sample mean or any xi is unbiased for mu but the have different distributions. Look up what is ment by MVUE.