I was wondering how do you find the density function of a random variable $Y$ given that :
$X$ is an arbitrary random variable.
$Y := X^2$
I know how to do that for the case where $X$ is continuous. But how would you that in the discrete case?
In the continuous case you would search for $ P(Y \leq y ) = P( X^2 \leq y ) $, and then when you found the distributition function, you just have to derivate it. But without this precious tool, what are the ways to conclude ?