[extropy-chat] what is probability?
gts
gts_2000 at yahoo.com
Tue Jan 16 16:29:04 UTC 2007
On Mon, 15 Jan 2007 18:44:23 -0500, Rafal Smigrodzki
<rafal.smigrodzki at gmail.com> wrote:
> ### I would see it this way: The meaning of "random" is "obeying the
> principle of indifference, where the sample space is unambiguously
> described". If the sample space is exactly two outcomes, then each one
> must occur 50% of the time, or else the coin is weighted, and the
> tosses are not quite random anymore.
Hmm, I think this is not at all what is or should be the definition of
"random".
As the word is normally defined, a series of tosses of an unfair coin
still result in a completely random sequence! How can you suggest
otherwise?
In objectivist terms, all that matters for the sake of randomness is that
the sequence satisfy what von Mises called "The Law of Excluded Gambling
Systems", which is just to say (roughly) that the sequence must contain no
predictable sub-sequences, i.e., that the result of each toss is
independent of the others. (Subjectivists have a different way of saying
essentially the same thing.)
-gts
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