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strange bound on correlation for symmetric pdf
I am puzzled by a rather simple fact:
The correlation of a symmetric multivariate pdf seems to be bound from below (increasingly strong with the number of dimensions). That seems unlikely to me.
But I ...
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Maximum possible correlation for $N$ random variables sharing idential correlation coefficient
Let $X_1, X_2, \ldots, X_n$ be random variables. For every $i\ne j$, assume $corr(X_i,X_j)=\rho$, where $\rho$ is some constant.
What is the maximum possible value of $\rho$?
- 840