Difference between max and min

Let \(U_1,U_2,U_3,U_4,U_5\) be independent, each with uiform distribution on \((0,1)\). Let \(R\) be the distance between the max and the min of the \(U_i\)’s. Find

  1. \(\mathbf{E} R\)
  2. the joint density of the max and the min of the \(U_i\)’s.
  3. the \(\mathbf{P}(R> .5)\)

[pitman p355, #14]

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