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FRM Part I · FRM Exam Part I · Random Variables

Random variable X has skewness of 1.2 and excess kurtosis of 4. Define Y = 3 - 2X. Which pair correctly gives the skewness and kurtosis (not excess kurtosis) of Y?

Y has skewness of -1.2 and kurtosis of 7. The negative coefficient flips the sign of skewness, while kurtosis, an even-power standardized moment, is unchanged. Excess kurtosis of 4 corresponds to kurtosis of 7, so the shift and scale do not alter it.

  1. ASkewness -1.2; kurtosis 7Correct
  2. BSkewness 1.2; kurtosis 7
  3. CSkewness -2.4; kurtosis 28
  4. DSkewness -1.2; kurtosis 4

Explanation

Skewness and kurtosis are standardized moments and are unaffected by positive scaling and shifts. A negative multiplier reverses the sign of skewness, giving -1.2. Kurtosis depends on even powers, so it is unchanged: excess kurtosis 4 means kurtosis 4 + 3 = 7. Option 4 confuses excess kurtosis with kurtosis, and option 3 wrongly scales the moments by the multiplier.

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