Kurtosis
= Kurtosis
{title2=$\kappa=\mathbb E[(X-\mathbb EX)^4]/\operatorname{Var}(X)^2$}
For finite <fourth moment> and positive <variance>, <kurtosis> is $\mathbb E[(X-\mathbb EX)^4]/\operatorname{Var}(X)^2$. The <normal distribution> has <kurtosis> $3$. A random scale can increase <kurtosis> even when the <conditional distribution> is normal.