Interview Question: Exponential Expectation

Sample Question #122 (probability theory)

If X ~ N(0, σ2), what’s E(eX)?

Hint: there’s a name for E(eX).

[Question courtesy of Dr. Yun Cheng of ITG]

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2 Responses to Interview Question: Exponential Expectation

  1. Brett says:

    ANSWER
     

    This is an example of a moment generating function. For this normal random variable, E(e^X) is the MGF for the 1st moment. The answer is e^[(σ^2)/2].  

  2. Jiangcheng says:

    MGF should be for the random variable itself.1st moment is MGF’s first derivative evaluated at t=0. So E(e^X) is the MGF evaluated at t=1, not MGF for the 1st moment.

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