[ 2009 FRM Sample Exam ] Quantitative Analysis Q9

jimgreen

 

9. 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?

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.

jimgreen

 

Correct answer is C

he skewness of both distributions is zero and the kurtosis of the student's t-distribution converges to that of the normal distribution as the number of degrees of freedom increases.

Reference: Schaum's Outline of Probability and Statistics, Spiegel, Schiller, and Srinivasan, 2000.

Type of Question: Quantitative Analysis