$\lim_{n \to \infty} E[\hat{\theta}_n] = \theta$ and $\lim_{n \to \infty} Var(\hat{\theta}_n) = 0$

$\hat{\theta}_n$ is the Maximum Likelihood Estimator for all finite $n$.

The Fisher Information $I(\theta)$ is finite for all $n$.

$\hat{\theta}_n$ is unbiased for all $n$.