Expectation of e raised to a normal

XX is standard normal. What is E[eX]E[e^{X}]? (to 4 decimals)

Show hints (2)+
  1. Use the normal MGF E[e^(tX)] = e^(t²/2).
  2. Evaluate at t = 1.

Answer

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1.6487 (± 0.005)

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