The random variables \(x\) and \(y\) are Gaussian with mean value 0 and variance 1 . Their covariance may be 0 or some know positive value \(r>0\). Show that the best choice between these possibilities on the basis of measurement of \(x\) and \(y\) depends on where the point \((x, y)\) lies with respect to a certain hyperbola in the \((x, y)\)-plane.