I am stuck with the following question:
There is a random variable $x\sim U[0,1] $. There are $n$ different draws (i.i.d.) being made. I am trying to compute the expected value/arithmetic mean of the $k$ highest of these draws.
That is, if I sort the draws $x_1\geq x_2\geq ...\geq x_n$, I am trying to compute $E[\frac{1}{k}\sum_{i=1}^kx_i]$.
While I have found this question on the expected value of the highest draw, I am unable to extend this to the average of the $k$ highes ones.