  We elucidate why the 1-Wasserstein distance $W_1$ coincides with the area
between the two marginal cumulative distribution functions (CDFs). We first
describe the Wasserstein distance in terms of copulas, and then show that $W_1$
with the Euclidean distance is attained with the $M$ copula. Two random
variables whose dependence is given by the $M$ copula manifest perfect
(positive) dependence. If we express the random variables in terms of their
CDFs, it is intuitive to see that the distance between two such random
variables coincides with the area between the two CDFs.
