$X_1$,$X_2$,$\cdots$,$X_n$为来自总体的$N(\mu_1,\sigma^2)$的简单随机样本,$Y_1$,$Y_2$,$\cdots$,$Y_m$,为来自总体的$N(\mu_2,2\sigma^2)$的简单随机样本,且两样本相互独立,记
$$\overline{X}=\dfrac{1}{n}\mathop{\Sigma}\limits_{i=1}^{n}X_{i},\overline{Y}=\dfrac{1}{m}\mathop{\Sigma}\limits_{i=1}^{m}Y_{i},S_1^2=\dfrac{1}{n-1}\mathop{\Sigma}\limits_{i=1}^{n}(X_i-\overline{X})^{2},S_{2}^{2}=\dfrac{1}{m-1}\mathop{\Sigma}\limits_{i=1}^{m}(Y_{i}-\overline{Y})^{2}$$
则
A. $\dfrac{S_1^2}{S_2^2}\sim F(n,m)$
B. $\dfrac{S_1^2}{S_2^2}\sim F(n-1,m-1)$
C. $\dfrac{2S_1^2}{S_2^2}\sim F(n,m)$
D. $\dfrac{2S_1^2}{S_2^2}\sim F(n-1,m-1)$