Consider the maximum-likelihood estimator $\tilde{\sigma}^{2}$ of $\sigma^{2}$ in the simple linear regression model. We know that $\tilde{\sigma}^{2}$ is a biased estimator for $\sigma^{2}$.

a. Show the amount of bias in $\tilde{\sigma}^{2}$.

b. What happens to the bias as the sample size $n$ becomes large?