设总体 $X \sim B(m, \theta), X_1, X_2, \cdots, X_n$ 为来自该总体的简单随机样本, $\bar{X}$ 为样本均值, 则 $E\left[\sum_{i=1}^n\left(X_i-\bar{X}\right)^2\right]=$
$\text{A.}$ $(m-1) n \theta(1-\theta)$.
$\text{B.}$ $m(n-1) \theta(1-\theta)$.
$\text{C.}$ $(m-1)(n-1) \theta(1-\theta)$.
$\text{D.}$ $m n \theta(1-\theta)$.