(統計) 母體混合期望值，變異數

設二母體，$\mu_1 ,\mu_2,\sigma_1^2,\sigma_2^2,n_1,n_2$

$\mu_i=\displaystyle\sum_{j=1}^{n_i}X_{ij}$  $,i=1,2$

$\sigma_i^2=\displaystyle\sum_{j=1}^{n_i}\cfrac{(X_{ij}-\mu_i)^2}{n_i}$ $,i=1,2$

混合期望值:$\mu_{混}=\cfrac{n_1\mu_1+n_2\mu_2}{n_1+n_2}$

混合變異數=$\sigma_{混}^2=\cfrac{\displaystyle\sum_{i=1}^{2}n_i\sigma_i^2+n_i\mu_i^2-n_i\mu_{混}^2}{\displaystyle\sum_{i=1}^{2}n_i}=\cfrac{\displaystyle\sum_{i=1}^{2}n_i[\sigma_i^2+(\mu_i-\mu_{混})^2]}{\displaystyle\sum_{i=1}^{2}n_i}$