Let X have a logistic distribution with p.d.f. f(x) = e^(-x)/(1 + e^(-x))^2 -infinty <x<infinity Show that Y = 1/(1 + e^(-x)) has a U (0, 1) distribution. (Hint: Find P (Y ≤ y) = P(1/(1 + e^(-x)<=y)
Follow Math Help Forum on Facebook and Google+
Originally Posted by affelix Let X have a logistic distribution with p.d.f. f(x) = e^(-x)/(1 + e^(-x))^2 -infinty <x<infinity Show that Y = 1/(1 + e^(-x)) has a U (0, 1) distribution. (Hint: Find P (Y ≤ y) = P(1/(1 + e^(-x)<=y) First note that since for . Then the cdf of Y is given by . Your job is to calculate this integral (for 0 < y < 1 the answer is y, by the way) and then calculate . Note also that details are important ....
View Tag Cloud