I have a small math problem
I have a sample of size N iid normal distributed variables. Then I get the MLE for mu and sigma^2(but the biased estimater for sigma^2, the one that is 1/N*(theRest) ). Now I have to prove consistecy of them both. Proving that for the unbiased estimator of mu is easy using Chebyshev.
My problem is proving the consistency of the biased MLE estimator of sigma^2.
Can anybody help me?