A note on the representation of {Eleft({textit{textbf {x}}}otimes {textit{textbf {xx}}}^{prime}right) } and {Eleft({textit{textbf {xx}}}^{prime }otimes {textit{textbf {xx}}}^{prime }right)} for the random vector x

In this paper we consider ${E(xotimes xx^{prime})}$ and ${E(xx^{prime }otimes xx^{prime})}$ for a random vector x where x _i has existing moments up to the fourth order and where the higher moments may depend on i. This extends previous results which assumed a common higher moment and E(xx??)?=?I.