Let X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1) and Y=eXY = e^XY=eX. What is the PDF of YYY?
fY(y)=yf_Y(y) = yfY(y)=y for 1≤y≤e1 \le y \le e1≤y≤e
fY(y)=0f_Y(y) = 0fY(y)=0 otherwise
fY(y)=1yf_Y(y) = \frac{1}{y}fY(y)=y1 for 1≤y≤e1 \le y \le e1≤y≤e
fY(y)=1f_Y(y) = 1fY(y)=1 for 1≤y≤e1 \le y \le e1≤y≤e