2次元正規分布
$ \boldsymbol{\mu}=\left(\begin{array}{l}{\mu_{1}} \\ {\mu_{2}}\end{array}\right), \Sigma=\left(\begin{array}{ll}{\sigma_{11}} & {\sigma_{12}} \\ {\sigma_{21}} & {\sigma_{22}}\end{array}\right)のときの正規分布$ N_2(\mu,\Sigma)を考える $ f\left(x_{1}, x_{2}\right)=\frac{1}{2 \pi \sigma_{1} \sigma_{2} \sqrt{1-\rho^{2}}} \exp \left\{-\frac{1}{2} D^{2}\right\}.
$ \rho=\frac{\mathrm{Cov}(X_1,X_2)}{\sqrt{V(X_1)}\sqrt{V(X_2)}}.
$ D^{2}=(\boldsymbol{x}-\boldsymbol{\mu})^{\prime} \Sigma^{-1}(\boldsymbol{x}-\boldsymbol{\mu}).