题目
设 X_1, X_2, X_3 是来自总体 X 的一个样本,且 E(X) = mu, D(X) = sigma^2,则下列估计量中是 mu 的无偏估计量的是()A. hat(mu) = (1)/(3)X_1 + (3)/(4)X_2 - (1)/(12)X_3B. hat(mu) = (1)/(3)X_1 + (3)/(4)X_2 + (1)/(12)X_3C. hat(mu) = (1)/(3)X_1 + (1)/(4)X_2 + (5)/(12)X_3D. hat(mu) = (1)/(5)X_1 + (3)/(10)X_2 + (1)/(2)X_3
设 $X_1, X_2, X_3$ 是来自总体 $X$ 的一个样本,且 $E(X) = \mu, D(X) = \sigma^2$,则下列估计量中是 $\mu$ 的无偏估计量的是()
A. $\hat{\mu} = \frac{1}{3}X_1 + \frac{3}{4}X_2 - \frac{1}{12}X_3$
B. $\hat{\mu} = \frac{1}{3}X_1 + \frac{3}{4}X_2 + \frac{1}{12}X_3$
C. $\hat{\mu} = \frac{1}{3}X_1 + \frac{1}{4}X_2 + \frac{5}{12}X_3$
D. $\hat{\mu} = \frac{1}{5}X_1 + \frac{3}{10}X_2 + \frac{1}{2}X_3$
题目解答
答案
ACD
A. $\hat{\mu} = \frac{1}{3}X_1 + \frac{3}{4}X_2 - \frac{1}{12}X_3$
C. $\hat{\mu} = \frac{1}{3}X_1 + \frac{1}{4}X_2 + \frac{5}{12}X_3$
D. $\hat{\mu} = \frac{1}{5}X_1 + \frac{3}{10}X_2 + \frac{1}{2}X_3$
A. $\hat{\mu} = \frac{1}{3}X_1 + \frac{3}{4}X_2 - \frac{1}{12}X_3$
C. $\hat{\mu} = \frac{1}{3}X_1 + \frac{1}{4}X_2 + \frac{5}{12}X_3$
D. $\hat{\mu} = \frac{1}{5}X_1 + \frac{3}{10}X_2 + \frac{1}{2}X_3$