Let X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1). What is the probability density function of Y=−2ln(X)Y = -2\ln(X)Y=−2ln(X)?
fY(y)=12e−y/2,y>0f_Y(y) = \frac{1}{2}e^{-y/2}, y > 0fY(y)=21e−y/2,y>0
fY(y)=2e−2y,y>0f_Y(y) = 2e^{-2y}, y > 0fY(y)=2e−2y,y>0
fY(y)=e−y,y>0f_Y(y) = e^{-y}, y > 0fY(y)=e−y,y>0
fY(y)=14ye−y/2,y>0f_Y(y) = \frac{1}{4}y e^{-y/2}, y > 0fY(y)=41ye−y/2,y>0