Let us assume we have two random variables $X$ and $Y$ where $X = f(A, B, C)$ and $Y = g(A, B, C)$. $A, B, C$ are 3 independent random variables and the functions $f, g$ are known but rather expensive to evaluate. Is there any fast method to compute or bound the Pearson correlation coefficient between of $X$ and $Y$ ?
What if the correlation coefficients between $X$ and $A, B, C$ and $Y$ and $A, B, C$ are given?
Thanks, Bogdan.