Given X∼U(0,1)X \sim U(0, 1)X∼U(0,1), what is the PDF of Y=−ln(X)Y = -\ln(X)Y=−ln(X)?
fY(y)=e−yf_Y(y) = e^{-y}fY(y)=e−y for y≥0y \geq 0y≥0
fY(y)=eyf_Y(y) = e^yfY(y)=ey for y≤0y \leq 0y≤0
fY(y)=1f_Y(y) = 1fY(y)=1 for 0≤y≤10 \leq y \leq 10≤y≤1
fY(y)=2e−2yf_Y(y) = 2e^{-2y}fY(y)=2e−2y for y≥0y \geq 0y≥0