  For two independent, almost surely finite random variables, independence of
their minimum (time) and the event that one of them is either greater, equal or
less than the other (cause) is completely characterized. It is shown that,
other than for trivial cases where, almost surely, one random variable is
greater than or equal to the other, this happens if and only if both random
variables are distributed like the same strictly increasing function of two
independent random variables, where either both are exponentially distributed
or both are geometrically distributed. This is then easily generalized to the
multivariate case.
