FRM Part I · FRM Exam Part I · Random Variables
For a random variable X, E[X] = 2, E[X^2] = 8 and E[X^3] = 44. What is the skewness of X?
Skewness is 1.50. The variance is 4, so the standard deviation cubed is 8. The third central moment is 44 minus 48 plus 16, which is 12. Dividing 12 by 8 gives 1.5.
- A1.50Correct
- B3.00
- C5.50
- D0.75
Explanation
Variance = 8 - 4 = 4, so sigma = 2 and sigma^3 = 8. Third central moment = E[X^3] - 3(mu)E[X^2] + 2mu^3 = 44 - 48 + 16 = 12. Skewness = 12/8 = 1.5. Using 12/4 = 3 divides by the variance, and 44/8 = 5.5 wrongly uses the raw third moment.
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