Estimators

In classical statistical inference, the data has some assumed distribution with parameters.
These parameters are unknown constants rather than random variables.
Estimators are functions of observed data that provide estimates of these parameters.

Expectation and variance are population concepts! They require full knowledge of the population distribution (PDF)

Bias

An estimator $\hat{\theta }$ is unbiased* if:
$E[\hat{\theta }]=\theta$

Consistency