Consider the following bounded variable $m_1$:
$a<m_1<x$
and the following bounded variable $m_2$:
$x<m_2<b$
where $a,b,x, m_1$ and $m_2$ are all real and positive.
Consider the function
$y=\frac{m_1}{m_2}$
Is there any way to do any inferences about the correlation between $x$ and $y$?
Thank you
The two given inequations imply $$\frac ab<y<1.$$
If you make a plot with the hidden variables $m_2,m_1$ for the axis, and draw a line from the origin, the slope is $y$. The locus of $(m_2,m_1)$ is a rectangle delimited by the verticals at $x$ and $b$, and the horizontals at $a$ and $x$. This rectangle is inscribed in the triangle defined by $a$, $b$ and the first bissector.
For a given $x$, the point can be anywhere in the rectangle and the slope can cover the full range $\left[\dfrac ab,1\right]$.
So without more constraints, $x$ and $y$ are completely independent.