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FRM Part I · FRM Exam Part I · Sample Moments

For a pair of random variables X and Y, how many distinct non-trivial coskewness measures exist, where the trivial cases are the skewness of X alone and of Y alone?

There are two distinct coskewness measures for a pair of variables: s(X,X,Y), which uses squared deviations of X times the deviation of Y, and s(X,Y,Y), which reverses the roles. Reordering factors gives nothing new, so the count is two.

  1. A1
  2. B2Correct
  3. C3
  4. D4

Explanation

Third-order cross moments with total power 3 that involve both variables are E[(X-μX)^2(Y-μY)] and E[(X-μX)(Y-μY)^2]. These are s(X,X,Y) and s(X,Y,Y), so there are two. Ordering of the factors does not create new measures.

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