Throughout the 20thcentury, probability has come to mean to two very
different things:
1) Frequency (a.k.a. a physical probability)
2) Uncertainty (a.k.a. a subjective probability)
It sometimes amazes me at how often this is pointed out, agreed upon, and
then forgotten. I would guess the main reason this happens is that same
mathematical tool can be used to either describe frequency in a population
of series XOR the uncertainty of a single value. It is often necessary to
examine the context of usage in order to figure out whether an equation (or
Bayes net) is representing frequency or uncertainty. If you have a value
that is both uncertain and variable then you have two dimensions, not one.
The problem with the phrase "random variable" is that it seems to rather
deliberately run the two concepts together (i.e. random = uncertain and
variable = frequency). I don't think this trick of sparing author and
audience the trouble of examining context is a good one. Any message using
the phrase "random variable" is unlikely to be the last -- some later
clarification will probably be necessary.
-Clark Carrington