For a random variable X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1), what is the variance of Y=eXY = e^XY=eX?
e2−12−(e−1)2\frac{e^2 - 1}{2} - (e-1)^22e2−1−(e−1)2
e2−12\frac{e^2 - 1}{2}2e2−1
e2−ee^2 - ee2−e
112\frac{1}{12}121