Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

Posted by Amit Goyal on Apr 13, 2010; 5:07am
URL: http://discussion-forum.276.s1.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p4894291.html

First of all, F(X) take values in the interval (0, 1) because F(.) is a cumulative distribution function. So, for 0 < a < 1 we have:
P(F(X) < a) = P(X < Finv(a)) (Since F is strictly increasing)
                = F(Finv(a)) = a
This implies that F(X) is distributed uniformly because Probability that F(X) take values less than a = a ∀ a ∈ (0, 1)