Sample Question #122 (probability theory)

If *X ~ N*(0, *σ*^{2}), what’s E(*e ^{X}*)?

Hint: there’s a name for E(*e ^{X}*).

[Question courtesy of Dr. Yun Cheng of ITG]

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Sample Question #122 (probability theory)

If *X ~ N*(0, *σ*^{2}), what’s E(*e ^{X}*)?

Hint: there’s a name for E(*e ^{X}*).

[Question courtesy of Dr. Yun Cheng of ITG]

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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].

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.