FRM Part I · FRM Exam Part I · Sample Moments
For two random variables X and Y, how many distinct non-trivial cross cokurtosis measures (those involving both variables, with the fourth-order moment taken about the means) exist?
There are three cross cokurtosis measures for two variables: K(X,X,X,Y), K(X,X,Y,Y) and K(X,Y,Y,Y). Each mixes X and Y in a fourth-order moment. The two-measure count applies to coskewness, not cokurtosis.
- A1
- B2
- C3Correct
- D4
Explanation
The cross fourth-order terms are K(X,X,X,Y), K(X,X,Y,Y) and K(X,Y,Y,Y). Pure terms such as K(X,X,X,X) are just the kurtosis of one variable. There are therefore three cross measures, not two (which is the count for coskewness).
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