Define the following two functions $Q$ and $S^2$:
One of the exercises now asks me to calculate the variance of $S^2$. I tried doing so with the help of a formula that makes use of the third and fourth centered moment and as far as I know, the fourth moment of a normally distributed variable with mean $\mu$ and variance $\sigma ^2$ is $3\sigma ^4$. In the solution; however, the author writes the following:
My question now is: Why would that be the case? From what does this follow? Both parts here are quite confusing to me; I don't see why it would be equal to $3\mu _2 ^2$ or equal to $3\sigma^2$ instead of $3\sigma ^4$.
(Source: Seber, 2003, Linear Regression Analysis)