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

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

[pitman p355, #14]