Order statistics are Beta

Among nn independent uniform [0,1][0,1] variables, what is the distribution of the kk-th smallest?

Show hints (2)+
  1. The k-th order statistic of uniforms is Beta-distributed.
  2. Its mean is k/(n+1).

Answer

Reveal answer →

Beta(k, n−k+1)\text{Beta}(k,\,n-k+1)

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