Financial Risk Manager Part 1
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The normal distribution and the lognormal distribution are related in such a way that:
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NNikitesh
A
If a random variable X follows a lognormal distribution, ln X is normally distributed
B
If a random variable X follows a normal distribution, ln X is said to have a lognormal distribution
C
The mean and variance of a lognormal distribution are twice that of the normal distribution, provided the value of n is the same
D
The mean and variance of the normal distribution are twice that of the lognormal distribution, provided the value of n is the same
Explanation:
A random variable X follows a lognormal distribution if its natural logarithm, ln X, is normally distributed. In layman's language (for easy understanding), you can view the term 'lognormal' as 'the log is normal'. This is the fundamental relationship between normal and lognormal distributions: if X is lognormally distributed, then ln(X) is normally distributed. Option B is incorrect because it reverses the relationship - if X is normally distributed, then e^X (not ln X) would be lognormally distributed. Options C and D are incorrect because the mean and variance relationships between normal and lognormal distributions are not simply twice each other; they follow specific formulas based on the parameters of the underlying normal distribution.
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