Statistics - Method of Moment Parameter Estimator

Question

Let X1, X2, X3, ..., Xn be a random sample of size n from the population with mean µ and variance σ² .

What is the estimator of the population parameter σ² if we use the moment method?

Answer 1

Recall that following variance formula:

Var(X) = E[X^2] - (E[X])^2

By law of large numbers, you can replace the expectation with the average. So, E[X^2] can be replaced by the average of X^2 and E[X] can be replaced by the average of X.