Let X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1) and Y=−ln(X)Y = -\ln(X)Y=−ln(X). What is the probability density function fY(y)f_Y(y)fY(y)?
fY(y)=e−y,y≥0f_Y(y) = e^{-y}, y \ge 0fY(y)=e−y,y≥0
fY(y)=1,0≤y≤1f_Y(y) = 1, 0 \le y \le 1fY(y)=1,0≤y≤1
fY(y)=ye−y,y≥0f_Y(y) = y e^{-y}, y \ge 0fY(y)=ye−y,y≥0
fY(y)=ey,y≤0f_Y(y) = e^y, y \le 0fY(y)=ey,y≤0