I think I understand the idea of coupling given here from page 18 - 20.I specially looked at the example. They are discussing the cases when given random variables have the same distribution with different parameters and in most they are also taking $P(X\leq Y)= 1$.
I want to ask if we have random variables with different distributions for example
$X$~$Poisson$ , $Y$~$Binomial$
$X$~$Exponential$ , $Y$~ $Geometric$
$\vdots$
and we can have $P(Y \leq X) = 1$.
How we are going to do Coupling in such cases and I am not sure how to provide the parameters for distributions. If some example is given that would be really helpful otherwise I would like to know intuition for such scenarios.