I'm having some difficulty finding the mean and the variance of the following question:
Let
be independent uniformly dist. r.v. on the interval
I found my density function for
kth order stat between 1 and n, which is:
where
now using what I found if I try to find the
I get:
where
=
where
now the integral looks a lot like a
Beta Function, but what puzzles me is that the beta function goes from 0 to 1, and I have 0 to
. If I were to make the substitution. I would get:
where
And for the
I get:
where
=
where
Again the first part of the integral looks like the
Beta Function, but since there's an additional y within it, I'm a little confused on how to integrate this out, since I don't think that a closed form of this function exists.