Uniform Spacing

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

1. \( E( R)\)
2. the joint density of the min and the max of the \(U\)’s
3. \(P( R>0.5)\)

[Pitman p. 355 #14]