and the cumulative distribution function is the identity between 0 and 1.So that applying the above formula for the

This is in fact a density we will encounter several times, it is the Beta(k,n-k+1) density.

Example:

Suppose five independent uniforms
*U*_{1}, *U*_{2}...*U*_{5}.

Find the joint density of *U*_{(2)} and*U*_{(4)} :

This is the density of which I showed you a picture in class when I defined joint densities, it is only non-zero for

0<*x*<*y*<1