TBan-I

Detour: Extreme Value Statistics

Definition of $n(x)$:

Given a realization, $n(x)$ is defined as the number of random variables above the minimum $E_{\min }$ such that their value is smaller than $E_{\min }+x$. This quantity is a random variable, and we are interested in its average value:

$\overline{n(x)}=\sum _{k}k\text{Prob}[n(x)=k]$