k-th order statistic

For five independent U[0,1]U[0,1] variables sorted ascending, what is the expected value of the 3rd smallest? (to 3 decimals)

Show hints (2)+
  1. n order statistics cut [0,1] into n+1 equal expected gaps.
  2. E[k-th of n] = k/(n+1).

Answer

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0.5 (± 0.005)

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