Let X,YX, YX,Y be jointly continuous. Can Cov(X,Y)Cov(X, Y)Cov(X,Y) and rho(X,Y)rho(X, Y)rho(X,Y) have opposite signs?
Yes, always if variances are undefined
No, they always have the same sign
Yes, if standard deviations are complex
No, correlation is standardized covariance