The following is a problem in my book that I don't really understand:
We take a random sample: $x_1,x_2,\ldots,x_n$ from a population that is $N(μ,σ)$ where $\mu$ and $\sigma$ are unknown.
We build two estimates:
$\mu^*_{\text{obs}} = \overline{x} = (x_1 + x_2 + \cdots + x_n)/n$
and
$\hat{\mu}^*_{\text{obs}} = (x_1+x_2)/2$
Show that both estimates are unbiased.
I know that an estimate of a sample mean is unbiased when we divide by $n-1$ instead of $n$. How come those two estimates are unbiased? In my eyes they are biased.