Correlation of min and max

For two i.i.d. Uniform(0,1)\text{Uniform}(0,1) variables, what is the correlation between their minimum and their maximum? (to 2 decimals)

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  1. Find Var(min), Var(max) and Cov(min,max).
  2. corr = Cov / sqrt(Var·Var).

Answer

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0.5 (± 0.01)

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