Finding the cdf of X = g(Y).

Hi All,

This is my first post here so be gentle.

I've the following question:

Suppose you have a parameter X, given by X=g(Y), that could only return

values in [0,1]. Y is a random variable and therefore X is also a random

variable. The probability that X=0 is p0, that X=1 is p1. I'd like to know

what's the cdf of X. In particular I know that F(X<=0)=p(X=0) and F(X>=1)=p

(X=1), but in between is a continuous cdf. How can I represent the cdf of X?

If I do it in the classical way for a continuous distribution I get F(X<=0)=0

and F(X>=1)=0...

Many thanks for your help!

Regards,

Joao