讲义中卡方分布的均值是k，方差2k，跟n是什么关系？

问题如下：

Which of the following statements about chi-square distribution and F-distribution is least likely correct?

选项：

A.

the expectation of the chi-square distribution is n, and the variance is 2n.

B.

Both of them are asymmetrical.

C.

Both of them are determined by their degree of freedom.

D.

Both of them have means which are smaller than their standard deviations.

解释：

D is correct.

考点：卡方分布和F分布

解析：因为卡方分布的均值是n，方差是2n，也就是说标准差是根号下2n。所以当n大于2时，它的均值是大于标准差的。至于F分布，因为它的方差中还有一个m，m的大小不知道，所以在题目已知条件下，F分布的均值和标准差没有明确大小关系。