I have some troubles with understanding of this explanation taken from wikipedia:
"An estimator can be unbiased but not consistent. For example, for an iid sample $\{x _1,..., x_n\}$ one can use $T(X) = x_1$ as the estimator of the mean $E[x]$. This estimator is obviously unbiased, and obviously inconsistent."
Why unbiased, and why inconsistent ...
Can someone explain it in more details?