Financial Risk Manager Part 1
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Which of the following are the most appropriate properties of normal distribution?
I. The mean, mode, and median are equal in a normal distribution.
II. The linear combination of two or more normally distributed random variables is not necessarily normally distributed.
III. The normal distribution has a skewness of 0 and excess kurtosis of 3.
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NNikitesh
A
II and III only
B
I only
C
II only
D
All the above
Explanation:
Explanation:
Let's analyze each statement:
I. The mean, mode, and median are equal in a normal distribution.
- TRUE - This is a fundamental property of the normal distribution. For a perfectly symmetric normal distribution, all three measures of central tendency (mean, median, mode) are equal.
II. The linear combination of two or more normally distributed random variables is not necessarily normally distributed.
- FALSE - This is actually incorrect. One of the key properties of normal distributions is that any linear combination of normally distributed random variables is also normally distributed. This property makes the normal distribution particularly useful in finance and statistics.
III. The normal distribution has a skewness of 0 and excess kurtosis of 3.
-
PARTIALLY FALSE - The normal distribution has:
- Skewness = 0 (correct)
- Kurtosis = 3 (correct for standard kurtosis)
- Excess kurtosis = 0 (not 3)
Excess kurtosis is defined as kurtosis minus 3. Since the normal distribution has kurtosis of 3, its excess kurtosis is 0.
Correct Answer Analysis:
- Only statement I is completely correct.
- Statement II is false.
- Statement III is partially incorrect (excess kurtosis is 0, not 3).
Therefore, the correct answer is B. I only.
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