I am looking for an example for two random variables that are dependent and sometimes explain the other one, but not in all cases. To be clear, I do not want two gaussian variables which are correlated and explain each other. I want it to be such that we can in some cases have information about $X$ from $Y$ while in other cases we have information about $Y$ from $X$ but these cases should be distinct.
I can (so far) only think of examples in which $X$ depends on $Y$ but not the other way around.
For example $X=\pm 1$ with certain probabilities and $Y=X^2$ means we can predict $Y$ from $X$ but not the other way around. Now I am looking for an example that has the properties that \begin{align*} Y\vert X\in A&\sim Y \\ Y| X \in B &\nsim Y \\ X|Y \in C &\sim X \\ X|Y \in D &\nsim X \end{align*} Where $A,B$ are subsets of the event space of $X$ and $C,D$ subsets of the event space of $Y$. If this does not exist, would you able to show me why not?