We now use a technique from high school algebra, completing the square, by recognizing that

2x2 — nax = i [x2 — 2nax] = ^ [(x — na)2 — n2a2] (3.90)

and we have thus shown that if Y is defined by Eq. (3.87), then E{Yn} = Anexp(n2a2/2), from which we can compute the mean and the variance.

This calculation also suggests that if we want to create a log-normally distributed random variable with a specified mean A, rather than using Eq. (3.87), we should use the definition

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