Let X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1). What is the variance of Y=eXY = e^XY=eX?
\frac{e^2-1}{2} - (e-1)^2
\frac{e^2-1}{2}
(e-1)^2
e^2 - e