This is the last machine learning question of the week. We’re going to expand on Day 2’s question, where you will recall we derived the maximum likelihood estimate of and for the multivariate case. (You should probably derive the maximum a posteriori estimate, also.)

Now, let’s go back to the univariate case, for simplicity’s sake. Is the maximum likelihood estimate of the variance a biased estimator? Why or why not? If it is not, then how would you determine the unbiased estimate of the parameters? What about the multivariate case with a covariance matrix?