The positive random variable X is said to be a log-normal random variable with parameters μ and σ2 if log(X) is a normal random variable with mean μ and variance σ2. Use the normal moment generating function to find the mean and variance of a lognormal

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The positive random variable X is said to be a log-normal random variable with parameters μ and σ2 if log(X) is a normal random variable with mean μ and variance σ2. Use the normal moment generating function to find the mean and variance of a lognormal random variable. Hint: Let Y = log(X ) and find E[X ].
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