This is not a classroom problem. This is a part of my own education.
Assume we have a random variable $X$ that is iid distributed according to the distribution $p$ that is defined as follows:
\begin{equation} p(X=x)=\frac{1}{2(x-1)^2}I_{\left[0,\frac{2}{3}\right]}(x) \end{equation}
Also, let $n \overset{iid}{\sim} U(3X,2)$.
We wish to determine the transformation:
\begin{equation} Y = \frac{n}{n+X} \end{equation}
This "$2X$" dependency in the $n$ distribution is throwing me off, and I am unsure how to begin this or similar problems. The transformation techniques I use do not involve dependencies such as this.
I attempted to gain some insight using Mathematica with the following script:
However, it gave me a nonsensical answer:
Any insight into how to solve this problem correctly would be great!