Re: Calculus XOR Probability

Matt Gutting said:
Tony Orlow wrote:
David R Tribble said:
Tony Orlow wrote:
I think if you are talking about a uniform probability distribution over the
naturals, you may have a point, but I don't think it exactly applies here.
Let's consider the vase, and we'll add ball 1 at 11:00, ball 2 at 11:30, ball 3
at 11:45, etc, so that all finite natural labeled balls are in the vase. Now
shake it at 12:00, and again at 12:30, then 12:45, etc. At 1:00, remove a ball
from the vase. Is there a uniform probability distribution, or are some of
those naturally-labeled balls more likely than others to be chosen?
Matt Gutting wrote:
I don't see that there's a probability distribution at all. What would be the
consequences of the existence of a probability distribution on this set?
If a probability distribution actually exists, then we can answer the
following questions:
1. If n values are chosen, what is their expected average value?
2. If a value x is chosen, what is the probability that the next
chosen value y is greater than x?

I don't see these having any answers, so the conclusion is that there
is no valid probability distribution.



Yes, you're right, over the finite naturals, of course. It seems impossible to
define what the range or count is, and trying to assume any such thing leads to
contradiction. Correct. Of course, in the above example, I can't see, despite
the inability of calculating any such numbers, that any ball has any different
chance than any other. If there is some set of balls in the vase, then whatever
size that set is, each ball has the reciprocal of that size as a probability.

Assuming that one can define a reciprocal for that number, okay. But how
does one compare the probability (say) of drawing one of the first ten balls
dropped in with the probability of drawing one of the first twenty? Can you
show that the numbers you use there exist?

If we have n balls, the probability of each is 1/n, and so the probability of
the ball being one of the first 10 is 10/n, as opposedto 20/n chance of it
being one of the first 20. If we have n=1:000...000, a megabigulous number,
then the inverse is 1/n, or 0:000...001 probability for each, 0:000...010 that
it be one of the first 10, or 0:000...020 that it be in the first 20.

Now, you want me to prove these numbers exist? I think if one creates a number
system, which is basically a language where each word represents a quantity,
then one can determine what operations are possible with it. The possibilities
are somewhat limited compared to finite arithmetic, but rational portions of
these quantities can certainly be represented using the connecting repeating
digit strings between limit points. Does that capability make the system
"exist"?


Matt
*** Posted via a free Usenet account from http://www.teranews.com ***


--
Smiles,

Tony
.

Relevant Pages

  • Re: Calculus XOR Probability
    ... at 11:45, etc, so that all finite natural labeled balls are in the vase. ... consequences of the existence of a probability distribution on this set? ... Yes, you're right, over the finite naturals, of course. ...
    (sci.math)
  • Re: A simple but confusing question
    ... In practice, the prior that you use, provided it is relatively flat, ... affects the probability of the next ball being white only for small n. ... knowledge concerning the proportion of white balls in the bucket; ...
    (sci.stat.math)
  • Re: Calculus XOR Probability
    ... at 11:45, etc, so that all finite natural labeled balls are in the vase. ... consequences of the existence of a probability distribution on this set? ... Yes, you're right, over the finite naturals, of course. ...
    (sci.math)
  • Re: A simple but confusing question
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    (sci.stat.math)
  • Re: Which is rarer?
    ... Comparing actual events to get the probability ... Waqar Younis takes a wicket every 30 balls ... A bowler can bowl a max of 60 deliveries. ... there are always four or more wickets left for him to take. ...
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