The second and fourth moments about mean are 4 and 48 respectively, then the distribution is:
A)Leptokurtic
B)Platykurtic
C)Mesokurtic or normal
D)Positively skewed

Question

Quizplus · Accepted Answer

The kurtosis of a distribution is determined by its fourth moment about the mean. For a normal distribution, the kurtosis (fourth moment about the mean) is 3 times the square of the variance (second moment about the mean). Given the second moment about the mean is 4, squaring this gives 16, and multiplying by 3 gives 48, which matches the given fourth moment. This indicates a mesokurtic or normal distribution.

The Second and Fourth Moments About Mean Are 4 and 48