Financial Risk Manager Part 1
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Q.3770 What are the conventional values of skewness and kurtosis of a normal random variable?
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TTanishq
A
Skewness=0, kurtosis=3
B
Skewness=1, kurtosis=3
C
Skewness=0, kurtosis=2
D
Skewness=0, kurtosis=4
Explanation:
Explanation
In a normal distribution:
Skewness = 0
- Skewness measures the asymmetry of a distribution
- A normal distribution is perfectly symmetrical
- Therefore, there is no skewness (skewness = 0)
Kurtosis = 3
- Kurtosis measures the 'tailedness' of a distribution
- A kurtosis of 3 indicates that the distribution has neither fat nor thin tails
- This is characteristic of a normal distribution
Why other options are incorrect:
Choice B is incorrect: Skewness of 1 implies significant asymmetry, which contradicts the symmetric property of a normal distribution.
Choice C is incorrect: Kurtosis of 2 indicates lighter tails and fewer outliers than the normal distribution, which is not characteristic of a normal random variable.
Choice D is incorrect: While higher kurtosis can indicate fat tails, for a standard normal random variable, the total kurtosis should be 3, not 4. Excess kurtosis (kurtosis above that of the normal distribution) should be zero.
Therefore, the conventional values of skewness and kurtosis for a normal random variable are 0 and 3, respectively.
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