You are definitely getting warm! But you are not quite there yet. —Dan
On Nov 4, 2015, at 1:13 PM, Seb Perez-D <sbprzd+mathfun@gmail.com> wrote:
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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun