Posted by haifeng on 2018-06-02 10:14:24 last update 2018-06-02 10:14:24 | Answers (1) | 收藏
性质. ($\chi^2$-分布的可加性)
若 $Y_1,Y_2,\ldots,Y_k$ 相互独立且都服从 $\chi^2$-分布, 自由度分别为 $n_1,n_2,\ldots,n_k$. 即
\[ Y_i\sim\chi^2(n_i),\quad i=1,2,\ldots,k, \]
则
\[ \sum_{i=1}^{k}Y_i\sim\chi^2(n),\quad\text{where}\ n=\sum_{i=1}^{k}n_i. \]
