Let X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1). Find the cumulative distribution function of Y=eXY = e^XY=eX.
ln(y)\ln(y)ln(y) for 1≤y≤e1 \le y \le e1≤y≤e
eye^yey for 0≤y≤10 \le y \le 10≤y≤1
yyy for 1≤y≤e1 \le y \le e1≤y≤e
\ln(y-1) for 1 \le y \le e