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!