On the maximum of bivariate normal random variables (Q1848529)

Let \((X,Y)\) be a bivariate Gaussian random vector with \(E X=\mu\), \(\operatorname{Var} X=\sigma^2\), \(\operatorname {Cov} XY=\eta\). Let \(Z=\max[X,Y]\). The author demonstrates that \(\partial E Z/\partial \sigma>0\), \(\partial E Z/\partial \eta<0\), but \(\partial \operatorname{Var} Z/\partial\mu\), \(\partial \operatorname{Var} Z/\partial\sigma\), \(\partial \operatorname{Var} Z/\partial\eta\) can be \(<\), \(=\) or \(>\) for different combinations of \((X,Y)\) parameters.