Editing Order statistic (section)

==== Proof ====
It can be shown that

: <math>B(k,n+1-k)\ \stackrel{\mathrm{d}}{=}\ \frac{X}{X + Y},</math>

where

: <math> X = \sum_{i=1}^{k} Z_i, \quad Y = \sum_{i=k+1}^{n+1} Z_i,</math>

with ''Z<sub>i</sub>'' being independent identically distributed [[exponential distribution|exponential]] random variables with rate 1. Since ''X''/''n'' and ''Y''/''n'' are asymptotically normally distributed by the CLT, our results follow by application of the [[delta method]].