NO.PZ2016062402000014
问题如下:
Which of the following statements is the most accurate about the relationship between a normal distribution and a Student’s t distribution that have the same mean and standard deviation?
选项:
A.They have the same skewness and the same kurtosis.
B.The Student’ t distribution has larger skewness and larger kurtosis.
C.The kurtosis of a Students t distribution converges to that of the normal distribution as the number of degrees of freedom increases.
D.The normal distribution is a good approximation for the Student’s t distribution when the number of degrees of freedom is small.
解释:
The two distributions have the same skewness of zero but the Student’ t has lower kurtosis. As the number of degrees of freedom increases, the Student’s t distribution converges to the normal distribution, so C is the correct answer.
t分布正常是比正态分布离散的,题目里说T和Z方差一致时,我理解就是n已经大到T趋近于Z的情况了,为什么A选项不对呢