Let \(U_1, U_2, U_3, U_4, U_5\) be independent uniform \((0,1)\) random variables. Let \(R\) be the difference between the max and the min of the random variables. Find

- \( E( R)\)
- the joint density of the min and the max of the \(U\)’s
- \(P( R>0.5)\)

[Pitman p. 355 #14]