Re: ISI INTERVIEW PREP

Posted by deepak on Jun 30, 2012; 2:45pm
URL: http://discussion-forum.276.s1.nabble.com/ISI-INTERVIEW-PREP-tp7578819p7578875.html

I'm nowhere close to being sure about this but here's what I tried :

y = F(x) = P(X<=x)
P(y<= a) = P(F(x) <=a)
Let's consider Finv(x) to be the inverse of F(x). Also, since F is increasing, Finv is also increasing.
so i can write this as
= P(Finv[F(x)] <= G(a) )
Since Finv(F(x) = x,
= P(x<=G(a))
this is the CDF's definition
= F(G(a))
again by definition of inverse
= a
ie P(y<=a) = a.
This must imply that y is a uniform distribution.