習題：
　　Exercise:
　　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.
　　解析：
　　Answer: C
　　Explanation: The two distributions have the same skewness of zero but the Student’s t has higher 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.
　　知識點：
　　Student’s t Distribution (t distribution)
　　If Z is a standard normal variable and U is a chi-square variable with k degrees of freedom, which is independent of Z, then the random variable X:
 
　　follows a t distribution with k degrees of freedom.
　　Properties：
　　l  The t distribution is symmetrical around its mean, which is equal to zero.
　　l  The variance of the t distribution for k > 2 is k/(k-2).
　　l  For low values of k, the t distribution looks very similar to a standard normal distribution, except that it displays excess kurtosis. As k increases, this excess kurtosis decreases. As k approaches infinity, the t distribution converges to a standard normal distribution.
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