Cumulative Conditional Mean - M(z)

Hi All,



I have a copula question! I'm surprised no one asked any questions on it yet.



For independent copulas: M(z) = 1/2



For all other copulas: M(1) = 1/2



Is that assuming that u,v in C(u,v) are uniformly distributed? I don't know why E(V/U < 1) = 1/2 unless u,v are assumed to be uniformly distributed.



Thanks!

Cumulative Conditional Mean - M(z)