Let X∼N(μ,σ2)X \sim N(\mu, \sigma^2)X∼N(μ,σ2). Find the expected value of eXe^XeX.
eμ+σ2/2e^{\mu + \sigma^2/2}eμ+σ2/2
eμe^{\mu}eμ
eμ+σ2e^{\mu + \sigma^2}eμ+σ2
e^{\mu - \sigma^2/2}