Gaussian fourth moment
= Gaussian fourth moment
{c}
{title2=$\mathbb E Z^4=3v^2$}
For a centered <normal random variable> $Z\sim N(0,v)$, $\mathbb EZ^4=3v^2$ and $\operatorname{Var}(Z^2)=2v^2$. This converts squared <normal> increments into exact <variance> calculations, including the degenerate case $v=0$.