$E[\hat{\theta}_n] = \theta$ and $Var(\hat{\theta}_n) \to 1$ as $n \to \infty$.

$Bias(\hat{\theta}_n) \to 0$ and $Var(\hat{\theta}_n) \to 0$ as $n \to \infty$.

The estimator $\hat{\theta}_n$ is the Maximum Likelihood Estimator.

$E[\hat{\theta}_n] = 0$ for all $n$.