Given 50 I.I.D Normal distributions random variables $X_i$, the Maximum Likelihood estimator for $\sigma^2$ is $\hat{\sigma}^2$, as proven in my lecture notes.
Find the EXACT SE.
My Attempt: SE of the estimate = SD of the estimator = SD($\hat{\sigma}^2$)
I am stuck. How do I even find the SD of the variance?
$(n-1)\frac{\hat \sigma^2}{\sigma^2}$ will be Chi-square distributed with n-1 degrees of freedom. So the SE will be the standard deviation of the associated Chi-squared distribution $\sqrt{2(n-1)}$ multiplied by $(\frac{\sigma^2}{n-1})^{1/2}$. Unfortunately, you will not know $\sigma^2$,so you will not know the standard error of the sample variance. However, you can still form confidence intervals for the true variance. This will have some useful information .