Let X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1). Find the variance of Y=e−XY = e^{-X}Y=e−X.
1−e−22\frac{1 - e^{-2}}{2}21−e−2
(1−e−1)2(1 - e^{-1})^2(1−e−1)2
12(1−e−1)2−(1−e−1)2\frac{1}{2} (1 - e^{-1})^2 - (1 - e^{-1})^221(1−e−1)2−(1−e−1)2 is incorrect, the correct form is 1−e−22−(1−e−1)2\frac{1 - e^{-2}}{2} - (1 - e^{-1})^221−e−2−(1−e−1)2
\frac{e^{-2} - 1}{2}