(2)比较$\frac{1}{\lambda }$的无偏估计 $\overline X$与$n.min ({X_1},{X_2},...,{X_n})$的有效性,正确的是()
A. 后者比前者更有效
B. 前者比后者更有效
C. 两者有效性一样
D. 无法比较
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${X_1},{X_2},...,{X_n}$是来自二项分布总体 X~b(n,p)的样本,用最大似然估计法估计参数p得()
A. $\frac{1}{n}\overline X $
B. $\frac{1}{n}(\overline X-1) $
C. $\frac{1}{n-1}\overline X $
D. $\frac{1}{n+1}\overline X $
设某种元件的使用寿命X的概率分布为$f(x;\theta ) = \left\{ {\begin{array}{*{20}{c}} {2{e^{ - 2(x - \theta )}},x \ge \theta }\\ {0,x< \theta } \end{array}} \right.$,其中${\theta>0}$为未知参数,${X_1},{X_2},...,{X_n}$为来自总体的简单随机样本,则$\theta$的矩估计为()
A. $\overline X-1$
B. $\overline X$
C. $\overline X-2$
D. $\overline X+2$
${X_1},{X_2},...,{X_n}$是来自均匀分布X~U(-a,a)的样本,用矩估计法估计参数a为()
A. ${(\frac{3}{n}\sum\limits_{k = 1}^n {x_k^2} )^{\frac{1}{2}}}$
B. ${(\frac{2}{n}\sum\limits_{k = 1}^n {x_k^2} )^{\frac{1}{2}}}$
C. ${(\frac{3}{n}\sum\limits_{k = 1}^n {x_k} )^{\frac{1}{2}}}$
D. ${(\frac{2}{n}\sum\limits_{k = 1}^n {x_k} )^{\frac{1}{2}}}$
${X_1},{X_2},...,{X_n}$是来自正态总体X~N($\mu$ ,${\sigma ^2}$)的样本,用估计法估 计参数$\mu,{\sigma^2}$,分别为()
A. $\overline X ,2{s^2}$
B. $2\overline X ,{s^2}$
C. $\overline X,{s^2}$
D. $\overline X,s$