From Osher Doctorow
Purely formally, suppose that we have:
1) f(x, y) = k on some interval or region
Adding 1 - fX(x) to both sides of (1) yields:
2) 1 + f(x, y) - fX(x) = P2(A-->B) = 1 + k - fX(x)
which says:
3) P2(A-->B) = (1 + k) - fX(x)
which is a simple linear function of fX(x).
The converse (that is, (3) implies (1)) also applies.
Readers can try a multiplicative example by considering the Bivariate
Gumbel distribution which I discussed in sci.physics Jan. 3, 2006, May
18, 2006, etc. (or look up Bivariate Gumbel as keywords in sci.physics
in the blank box near the heading).
Osher Doctorow
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