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Let ''B(k)'' (resp. ''H(k)'') be the event "there is right-to-left minimum (resp. maximum) at rank ''k''", i.e. ''B(k)'' is the set of the permutations <math>\scriptstyle\ \mathfrak{S}_n</math> which exhibit a right-to-left minimum (resp. maximum) at rank ''k''. We clearly have
<center><math>\{\omega\in B(k)\}\Leftrightarrow\{L(k,\omega)=
Thus the number ''N<sub>b</sub>(ω)'' (resp. ''N<sub>h</sub>(ω)'') of right-to-left minimum (resp. maximum) for the permutation ''ω'' can be written as a sum of independent [[Bernoulli random variable]]s each with a respective parameter of 1/k :
<center><math>N_b(\omega)=\sum_{1\le k\le n}\ 1\!\!1_{B(k)}\quad\text{and}\quad N_b(\omega)=\sum_{1\le k\le n}\ 1\!\!1_{H(k)}.</math></center>
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