3.3.1 The Chi-square Distribution

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Corollary 3.3.1

Let $X_1,\dots ,X_n$ : Independent random variables

Suppose $X_i\sim {\chi }^2(r_i),\forall i=1,\dots ,n$

Then $Y={\sum }_{i=1}^n{X}_i\sim {\chi }^2\left({\sum }_{i=1}^n{r}_i\right)$