数学试题讲解

设总体

X \sim N (μ, σ^{2}), X_{1}, X_{2}, \dots, X_{n}

为来自总体

X

的简单随机样本,

\bar{X} = \frac{1}{n} \sum_{i = 1}^{n} X_{i}

, 已知

k \sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2}

为

σ^{2}

的无偏估计量, 则

k =

\frac{1}{n}

\frac{1}{2 n}

\frac{1}{2 (n - 1)}

\frac{1}{n - 1}