For a random variable X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1), define Y=−ln(X)Y = -\ln(X)Y=−ln(X). What is the moment generating function MY(t)M_Y(t)MY(t)?
(1-t)^{-1} for t < 1
(1+t)^{-1} for t > -1
e^{t^2/2}
1/(1-t^2)