R=-1/sqrt(3) My proof is rather pedestrian, and involves proving that the variance-covariance matrix, with 1 on the diagonal and R off, is positive semi-definite. X can be constructed as U1+R*(U2+U3+U4) (and the others by permutation), where the Ui are independent, zero-mean random variables of equal variance. Cheers, Sébastien On Nov 3, 2015 22:02, "Dan Asimov" <asimov@msri.org> wrote: Suppose X, Y, Z, W are real random variables with a joint distribution such that each one has a finite mean and standard deviation. Suppose that all pairs of these random variables have the same correlation coefficient:* R = rho(X,Y) = rho(X,Z) = rho(X,W) = rho(Y,Z) = rho(Y,W) = rho(Z,W) . Find the minimum possible value of R. —Dan ____________________________________ * The definition of the correlation coefficient rho(U,V) of two random variables U and V is the expected product of their standardizations: rho(U,V) = E( ((U-mu_U)/sigma_U) * ((V-mu_V)/sigma_V)) ) where E is expectation, mu denotes mean and sigma denotes standard deviation. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun