CEO Salary Estimation Problem
Consider the following problem. An investigative reporter wants to figure out how much salary makes the CEO of an investment bank X. For this he conducts interviews with some of the employees of that bank and writes down their salaries, which forms the following sample

Consistent Estimators
In the estimation problem of a one-dimensional parameter \(\theta\) from an i.i.d. sample \[X^n=(X_1,\cdots,X_n),\ \ X_i\sim F(x,\theta),\,\theta\in\Theta\subset R\]
we introduced the notion of consistency of an estimator.
This means that whatever the unknown value of \(\theta\) is, this estimator is going to be close to that value in higher probability as \(n\) increases
\[\hat\theta_n\approx\theta, \text{ for large } n.