数学试题讲解

设总体

X

服从参数为

λ (λ > 0)

的泊松分布,

X_{1}, X_{2}, \dots, X_{n} (n ⩾ 2)

为来自该总体的简单随机样本, 则对于统计量

T_{1} = \frac{1}{n} \sum_{i = 1}^{n} X_{i}, T_{2} = \frac{1}{n - 1} \sum_{i = 1}^{n - 1} X_{i} + \frac{1}{n} X_{n}

, 有

E (T_{1}) > E (T_{2}), D (T_{1}) > D (T_{2})

. B.

E (T_{1}) > E (T_{2}), D (T_{1}) < D (T_{2})

. C.

E (T_{1}) < E (T_{2}), D (T_{1}) > D (T_{2})

. D.

E (T_{1}) < E (T_{2}), D (T_{1}) < D (T_{2})