random

[Alex Martelli]

"David C. Ullrich" <ullrich at math.okstate.edu> wrote in message
news:3b1e3e18.160819 at nntp.sprynet.com...
    ...
> Answer the question instead of only replying
> to the parts you feel like replying to.

This thread is long enough without going around
commanding each other what to answer, but for
once I'll make an exception:-) [not fully
responding to this post -- yet -- but only to
the 'mandatory' parts:-)]:

> _Do_ you think it makes sense to talk about
> the probability that the first digit of pi
> is 3?

Yes!  Or rather it makes sense to talk of
    P(first digit of pi is 3 | y)
for any y representing (if I recall De
Finetti's formula correctly) "a self-consistent
set of beliefs about the state of the Universe".

I do not believe that it REALLY makes sense
to talk about any P(x), rather than P(x|y),
unless the y can reasonably be taken as
given by the context.  I do realize that for
some strange reasons this De Finetti idea
is not universally accepted (yet:-), but
it IS widely accepted enough among scholars
of probability theory that I don't think I
need to defend it in depth -- or is my hope
unfounded and do we need to branch off into
ANOTHER huge subthread about whether
_unconditional_ probabilities "exist"...?-)


> (Or rather: Does it really make sense
> to say that the probability that the first
> digit of pi is 1/10?)

It surely "makes sense" (like many false
statements can "make sense") but may be
false for any y, if we carefully constrain
all relevant definitions (i.e., it is quite
possible that no y such that the P(x|y),
for the x we've been talking about, which
is self-consistent in the De Finetti sense).


Alex