I've had problems working this out:
Let be N independent uniform distributed variables that is are all iid uniform[0,1].
Define: for all i=1,...,N
That is, is the ratio of one of the variables divided by the sum of all variables, so that
I'm looking for the
- expected value: . I'm 99% sure this is equal to 1/N.
- variance:
- covariance:
I would be very grateful for all help!
Let me add the final percent: you have by symmetry hence
. (To Anonymous: you can't compute the expectation like you did!)
So you need . I'm not sure you can't avoid computing the -fold integral . Did you already try?- variance:
This one can follow from the previous one, in a similar way to .- covariance: