设(X)_(1),(X)_(2),... ,(X)_(n)和(Y)_(1),(Y)_(2),... ,(Y)_(m)分别是来自两个独立的正态总体N((mu )_(1),({sigma )_(1)}^2)，N((mu )_(2)，(sigma )_(2)^2)的样本，则dfrac(1)({{sigma )_(1)}^2}sum _(i=1)^n(({X)_(i)-overline(X))}^2+dfrac(1)({{sigma )_(2)}^2}sum _(i=1)^m(({Y)_(i)-overline(Y))}^2服从的分布是( )A、t(m+n)B、(chi )^2(m+n)C、(chi )^2(m+n-2)D、F(m,n)

设${X}_{1},{X}_{2},\cdots ,{X}_{n}$和${Y}_{1},{Y}_{2},\cdots ,{Y}_{m}$分别是来自两个独立的正态总体$N\left({\mu }_{1},{{\sigma }_{1}}^{2}\right)$，$N({\mu }_{2}，{\sigma }_{2}^{2})$的样本，则$\dfrac{1}{{{\sigma }_{1}}^{2}}\sum _{i=1}^{n}{({X}_{i}-\overline{X})}^{2}+\dfrac{1}{{{\sigma }_{2}}^{2}}\sum _{i=1}^{m}{({Y}_{i}-\overline{Y})}^{2}$服从的分布是(   )

$A、t(m+n)$

$B、{\chi }^{2}(m+n)$

$C、{\chi }^{2}(m+n-2)$

$D、F\left(m,n\right)$