Prove that the expectation and the variance of a lognormal random variable X with mean μ, standard deviation σ, and a normal random variable W with mean 0, standard deviation σ, have the following relation:
(Note: You must prove the relation from both sides)
E(X) = e^(μ+σ^2/2)
Var(X) = (e^(σ^2)-1)e^(2μ+σ^2)
W = N(0, σ)