let X and Y be two continuous random variables with uniform distribution in the same interval [a;b].
They are correlated with a given correlation coefficient $\rho$.
I'm curious if there is the analytical opportunity to evaluate the joint probability density $f(x,y)$.
It is equal to $f(x,y) = f(x)\cdot f(y|x)$ but suppose $f(y|x)$ is unknown.
There are similar questions but:
- many of them (for instance 1, 2) refer to the standard distribution
- others tell that knowing $\rho$ is not sufficient to find the conditional probability density
Well, if it is true, I wanted to know which is the missing information and understand why $\rho$ is not sufficient. Maybe, there is the opportunity to estimate the missing part. Or maybe there exists some specific properties of the uniform distribution.