题目
4、设总体Xsim N(mu,sigma^2)，X_(1),X_(2),...,X_(n)是X的样本，overline(X)，S^2是样本均值和样本方差，则下列式子中不正确的有（）A. (sum_(i=1)^n(X_(i)-overline(X))^2)/(sigma^2)simchi^2(n-1)B. (overline(X)-mu)/(sigma)sim N(0,1)C. (overline(X)-mu)/(S/sqrt(n))sim t(n-1)D. (sum_(i=1)^n(X_(i)-mu)^2)/(sigma^2)simchi^2(n)
4、设总体$X\sim N(\mu,\sigma^{2})$，$X_{1},X_{2},\cdots,X_{n}$是X的样本，$\overline{X}$，$S^{2}$是样本均值和样本方差，则下列式子中不正确的有（）
A. $\frac{\sum_{i=1}^{n}(X_{i}-\overline{X})^{2}}{\sigma^{2}}\sim\chi^{2}(n-1)$
B. $\frac{\overline{X}-\mu}{\sigma}\sim N(0,1)$
C. $\frac{\overline{X}-\mu}{S/\sqrt{n}}\sim t(n-1)$
D. $\frac{\sum_{i=1}^{n}(X_{i}-\mu)^{2}}{\sigma^{2}}\sim\chi^{2}(n)$
题目解答
答案
B. $\frac{\overline{X}-\mu}{\sigma}\sim N(0,1)$