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 Apr 25 awarded Notable Question Mar 16 revised Expectation of a function of $Beta$ random variables added 14 characters in body Mar 14 revised Expectation of a function of $Beta$ random variables edited tags Mar 14 asked Expectation of a function of $Beta$ random variables Feb 23 accepted Two equations with $2n$ variables Feb 22 comment Two equations with $2n$ variables @zhoraster, see my answer. Feb 22 answered Two equations with $2n$ variables Feb 21 comment Two equations with $2n$ variables No, no additional constraints. And $n$ can be any positive integer. Feb 21 comment Two equations with $2n$ variables @zhoraster, not necessarily. For instance, for $n=1$ we obviously get $p_1=q_1$. Feb 21 asked Two equations with $2n$ variables Feb 21 revised $\lim\limits_{n\to\infty}\operatorname{Var}(n^{-1}\sum_{i=1}^{n}X_i)$ added 125 characters in body Feb 20 comment $\lim\limits_{n\to\infty}\operatorname{Var}(n^{-1}\sum_{i=1}^{n}X_i)$ OK, so instead of $E(W)$ we will have $Sum(E[W_i])/n$, right? And the condition for $S=0$ would be $Sum(E[W_i])/n=Sum(E[X_i])/n=Sum(E[Z_i])/n$, right? Feb 20 comment $\lim\limits_{n\to\infty}\operatorname{Var}(n^{-1}\sum_{i=1}^{n}X_i)$ @A.S, could you address a new case I have in this setting: say $W,X,Z$ are each a sequence of RVs, $W_i, X_i, Z_i, i:1...n$ instead of single RVs, and I sample $n$ values from one of these sequences (again according to the prior probabilities), independently but thus not identically distributed. I would like again to find $S$, and the condition for which it would be zero, this time in terms of $E(W_i), E(X_i), E(Z_i), i:1...n$ (and the prior probabilities). Feb 19 awarded Critic Feb 19 revised $\lim\limits_{n\to\infty}\operatorname{Var}(n^{-1}\sum_{i=1}^{n}X_i)$ There was a typo Feb 19 suggested approved edit on $\lim\limits_{n\to\infty}\operatorname{Var}(n^{-1}\sum_{i=1}^{n}X_i)$ Feb 19 accepted $\lim\limits_{n\to\infty}\operatorname{Var}(n^{-1}\sum_{i=1}^{n}X_i)$ Feb 19 comment $\lim\limits_{n\to\infty}\operatorname{Var}(n^{-1}\sum_{i=1}^{n}X_i)$ yes thanks that looks correct. Feb 19 comment $\lim\limits_{n\to\infty}\operatorname{Var}(n^{-1}\sum_{i=1}^{n}X_i)$ @A.S: Thanks! Looks OK to me. Feb 19 comment $\lim\limits_{n\to\infty}\operatorname{Var}(n^{-1}\sum_{i=1}^{n}X_i)$ @A.S, thanks for your comment, but it is not all clear how to find the parameters in your solution. Ultimately I need an expression for $S$ in terms of the means of $W,Y,Z$ and the prior probabilities. Can you write your answer as an "answer" not comment...?