Unbiasedness

Definition 8..1
For a random sample $X_1, \ldots, X_n$ from $f(x;\theta)$, a statistic $T=t(X_1, \ldots,X_n)$ is an unbiased estimator of $\theta$ if $E(T)=\theta$.

Definition 8..2
The bias in T (as an estimator or $\theta$) is

$$b_T(\theta)=E(T)-\theta.$$ (8.1)