Finding the cdf of X = g(Y).
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
Many thanks for your help!