Hello,

This is a very common problem. I'm copying it from something I typed before, so don't worry if the are transformed into X.

(set of permutations) because the random variables are iid.

Considering the permutation that inverts 1 and k for some k, we obtain that has the same distribution as .

So , the follow the same distribution.

Now consider the function :

and apply it to the vectors .

It follows that are identically distributed for all k.

In particular, it follows that .

Hence