Let X∼Exponential(λ)X \sim \text{Exponential}(\lambda)X∼Exponential(λ). What is the variance of Y=eXY = e^XY=eX?
λ2(λ−1)2(λ−2)\frac{\lambda^2}{(\lambda-1)^2(\lambda-2)}(λ−1)2(λ−2)λ2
λ(λ−1)2\frac{\lambda}{(\lambda-1)^2}(λ−1)2λ
1(λ−1)2(λ−2)\frac{1}{(\lambda-1)^2(\lambda-2)}(λ−1)2(λ−2)1
Does not exist for λ≤2\lambda \le 2λ≤2