Given X₁ = N (0,1)and X₂ = N (0.5,8),what is the mean of eˣ²?

Name: Given X₁ = N (0,1)and X₂ = N (0.5,8),what is the mean of eˣ²?
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Question

Quizplus · Accepted Answer

We know that if X~N(μ,σ²), then E(e^X) = e^(μ+σ²/2).
So, for X₁, E(e^(X₁²)) = e^(0+1/2) = e^(1/2).
For X₂, E(e^(X₂²)) = e^(0.5+8/2) = e^(4.25).

Therefore, the mean of e^(X₁²) + e^(X₂²) is e^(1/2) + e^(4.25) which equals approximately 79.97.