设$\pmb{x}$为$n \times 1$维度的随机向量，记$\pmb{A}$为$n \times n$维度的矩阵，并设
\[E[\pmb{x}] = \pmb{\mu}\] \[Var[\pmb{x}] = \pmb{\Sigma}\]则由如下等式成立:
\[E[\pmb{x}^T A \pmb{x}] = tr(\pmb{A}\pmb{\Sigma}) + \pmb{\mu}^T A \pmb{\mu}\]设$\pmb{x}$为$n \times 1$维度的随机向量，记$\pmb{A}$为$n \times n$维度的矩阵，并设
\[E[\pmb{x}] = \pmb{\mu}\] \[Var[\pmb{x}] = \pmb{\Sigma}\]则由如下等式成立:
\[E[\pmb{x}^T A \pmb{x}] = tr(\pmb{A}\pmb{\Sigma}) + \pmb{\mu}^T A \pmb{\mu}\]