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Assume that log X ~ N(0, 1). What is the expectation of X?
This is the same question as problem #35 in the Statistics Chapter of Ace the Data Science Interview!
Define . We then want to solve for:
Recall that a moment generating function has the following form:
Therefore, we want the moment generating function for , which was derived in this question and has the form:
Therefore, evaluating at (since we want the mean) gives:
which is the desired answer.