Let X have a logistic distribution with pdf f(x)=e−x/(1+e−x)2, −∞ < x< ∞. Show that
Y=1/1+e−X has a U(0, 1) distribution. Hint: Find G(y) = P(Y≤y)=P(1/1+e−X ≤ y)
when 0 < y < 1.
Let X have a logistic distribution with pdf f(x)=e−x/(1+e−x)2, −∞ < x< ∞. Show that
Y=1/1+e−X has a U(0, 1) distribution. Hint: Find G(y) = P(Y≤y)=P(1/1+e−X ≤ y)
when 0 < y < 1.