# The Log Normal Distribution

The Log Normal Distribution

If is a normal random variable with parameters and , then is a log normal random variable with the same parameters. Note that and are not the mean and standard deviation of . Just as (by the central limit theorem) the sum of a large number of independent, identically distributed random variables is nearly normal, the product of a large number of independent, identically distributed random variables is nearly log normal. The red vertical line marks the mean of the distribution.

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