Let $X_1,X_2$,....,be a random sample from $N(q,w^2)$; $q,w$ are unknown. Let $S_n$ be the sample standard deviation.
What is $Var(S_n^2)$? and how to show that $S_n^2$ is asymptotically normal?
I tried to do Variance part using moment generating functions but expressions are getting extremely complicated.