{\rm E}\left[ {{{\partial ^2 z} \over {\partial x_1 \partial x_2 }}\left( {x_1 - \,\,\bar x_1 } \right)\left( {x_2 - \,\,\bar x_2 } \right)} \right]\,\,\, = \,\,\,{{\partial ^2 z} \over {\partial x_1 \partial x_2 }}\,{\rm E}\left[ {\left( {x_1 - \,\,\bar x_1 } \right)\left( {x_2 - \,\,\bar x_2 } \right)} \right]\,\,\, = \,\,\,{{\partial ^2 z} \over {\partial x_1 \partial x_2 }}\sigma _{1,2}
