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**Per** I've had problems working this out:

Let $\displaystyle z_1,...,z_N$ be N independent uniform distributed variables that is $\displaystyle z_1,...,z_N$ are all iid uniform[0,1].

Define: $\displaystyle s_i = z_i/(z_1+...+z_N) $ for all i=1,...,N

That is, $\displaystyle s_i $ is the ratio of one of the variables divided by the sum of all variables, so that $\displaystyle s_1+...+s_N = 1 $

I'm looking for the

- expected value: $\displaystyle E[s_i] $. I'm 99% sure this is equal to 1/N.

- variance: $\displaystyle VAR[s_i] $

- covariance: $\displaystyle COV[s_i,s_j] $

I would be very grateful for all help!