题目
10【多选题】设X_(1),X_(2),...,X_(n)是来自总体Xsim N(mu,sigma^2)的样本，其中μ已知，则下列（）是σ²的无偏估计量.A. hat(sigma)_(1)^2=(1)/(n)sum_(i=1)^n(X_(i)-mu)^2B. hat(sigma)_(2)^2=(1)/(n-1)sum_(i=1)^n(X_(i)-mu)^2C. hat(sigma)_(3)^2=(1)/(n-1)sum_(i=1)^n(X_(i)-bar(X))^2D. hat(sigma)_(4)^2=(1)/(n)sum_(i=1)^n(X_(i)-bar(X))^2
10【多选题】设$X_{1},X_{2},\cdots,X_{n}$是来自总体$X\sim N(\mu,\sigma^{2})$的样本，其中μ已知，则下列（）是σ²的无偏估计量.
A. $\hat{\sigma}_{1}^{2}=\frac{1}{n}\sum_{i=1}^{n}(X_{i}-\mu)^{2}$
B. $\hat{\sigma}_{2}^{2}=\frac{1}{n-1}\sum_{i=1}^{n}(X_{i}-\mu)^{2}$
C. $\hat{\sigma}_{3}^{2}=\frac{1}{n-1}\sum_{i=1}^{n}(X_{i}-\bar{X})^{2}$
D. $\hat{\sigma}_{4}^{2}=\frac{1}{n}\sum_{i=1}^{n}(X_{i}-\bar{X})^{2}$
题目解答
答案
AC
A. $\hat{\sigma}_{1}^{2}=\frac{1}{n}\sum_{i=1}^{n}(X_{i}-\mu)^{2}$
C. $\hat{\sigma}_{3}^{2}=\frac{1}{n-1}\sum_{i=1}^{n}(X_{i}-\bar{X})^{2}$
A. $\hat{\sigma}_{1}^{2}=\frac{1}{n}\sum_{i=1}^{n}(X_{i}-\mu)^{2}$
C. $\hat{\sigma}_{3}^{2}=\frac{1}{n-1}\sum_{i=1}^{n}(X_{i}-\bar{X})^{2}$