Figure 1.

(Color online) Left panel: A plot of the curve $\gamma (t)$ used to visualize the joint cumulative density function, $W(x,y)$, of values of the functions $f(t)$ and $g(t)$. The probability density is non-zero only on the curve $\gamma (t)$ because the random variables $X=f(t)$, $Y=g(t)$are concentrated exclusively on $\gamma (t)$. On the right is an graphical calculation of $W(x,y)$ using the graphs of $f(t)$ and $g(t)$. The exact definition of $W(x,y)$ is given in Eq.B1.