题目
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's t-distribution has larger skewness and larger kurtosis.
C.The kurtosis of a Student's 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.
答案
C
解析
The two distributions have the same skewness of zero but the Student's t-distribution has higher kurtosis. As the number of degrees of freedom increases, the Student converges to the normal, so C is the correct answer. 两种分布的偏度相同为零，但学生t分布的峰度更高。随着自由度数量的增加，学生t趋向于正态分布，因此C是正确的答案。