Re: Probability in an infinite sample space
- From: Dave Seaman <dseaman@xxxxxxxxxxxx>
- Date: Mon, 20 Mar 2006 03:21:41 +0000 (UTC)
On 19 Mar 2006 19:04:41 -0800, mikeh106@xxxxxxxxxxx wrote:
If you choose a natural number at random, that it will be a multiple of
3 is there a 1/3, 1/2, or undefined chance?
That's a meaningless question, because you have not identified a
probability distribution.
It is often assumed that if no distribution is specified, then a uniform
distribution is intended. That can't be the case here, because there is
no such thing as a uniform probability distribution on a countably
infinite sample space.
Does it mean something to select "at random" from an infinite number of
objects?
Certainly, provided a probability distribution is specified. For
example, there is a uniform distribution on the unit interval [0,1],
which is an uncountably infinite space. You can also have a probability
distribution on a countably infinite space, but it can't be uniform. For
example, the probability might be P(n) = 2^(-n) for n = 1, 2, 3, ....
--
Dave Seaman
U.S. Court of Appeals to review three issues
concerning case of Mumia Abu-Jamal.
<http://www.mumia2000.org/>
.
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