表示

$$ (X,Y) \sim N(\mu_{X}, \mu_{Y}, \sigma^{2}{X},\sigma^{2}{Y}, \rho_{XY}) $$

联合概率密度

$$ f(x,y)=\frac{1}{2\pi\sigma_{1}\sigma_{2}\sqrt{ 1-\rho^{2} }} \exp\left{ \frac{1}{2(1-\rho^{2})} \left(\frac{x^{2}}{\sigma_{1}^{2}}+\frac{xy}{2\sigma_{1}\sigma_{2}}+\frac{y^{2}}{\sigma_{2}^{2}}\right) \right} $$