连续型二维求分布函数

二维均匀分布

在平面有界区域 D 上服从均匀分布，概率密度为 \(f(x, y)= \begin{cases}\frac{1}{S_{D}}, & (x, y) \in D . \\ 0, & \text { 其他 },\end{cases}\) image-20210814100431838

二维正态分布

  1. 若 $\left(X_{1}, X_{2}\right) \sim N\left(\mu_{1}, \mu_{2}: \sigma_{1}^2+\sigma_{2}^2 ; \rho\right)$​，则
\[X_{1} \sim N\left(\mu_{1}, \sigma_{1}^{2}\right), X_{2} \sim N\left(\mu_{2} \cdot \sigma_{2}^{2}\right)\]
  1. 若 ${X_{1} \sim N\left(\mu_{1}, \sigma_{1}^{2}\right), X_{2} \sim N\left(\mu_{2} \cdot \sigma_{2}^{2}\right)}$​ 且 ${X_1,X_2}$ 相互独立，则
\[\left(X_{1}, X_{2}\right) \sim N\left(\mu_{1}, \mu_{2}: \sigma_{1}^2+\sigma_{2}^2 ; 0\right)\]

:pill: 注

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