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Topic: Continuous and discrete uniform distributions of N
Replies: 27   Last Post: Dec 28, 2012 9:45 PM

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 Butch Malahide Posts: 894 Registered: 6/29/05
Re: Continuous and discrete uniform distributions of N
Posted: Dec 25, 2012 4:57 AM

On Dec 25, 3:12 am, Virgil <vir...@ligriv.com> wrote:
> In article
>  Butch Malahide <fred.gal...@gmail.com> wrote:
>

> > On Dec 25, 12:48 am, Virgil <vir...@ligriv.com> wrote:
>
> > > The standard definition of probability requires that the sum of the
> > > probabilities over ANY set of sets making up a partition of the space be
> > > equal to one.

>
> > How does that work out in the case of the partition of the space into
> > its one-element subsets?

>
> If the space is N, it doesn't, which is teh point I was trying to bring

You said "The standard definition of probability requires that the sum
of the probabilities over ANY set of sets making up a partition of the
space be equal to one." If the probability space is the unit interval
with Lebesgue measure, your "standard requirement" fails in the case
of the partition into one-element sets.

> > Are you saying that the standard definition
> > requires every probability distribution to be discrete?

>
> Not at all! Finite spaces cause no problems and for a space of
> uncountable cardinality, one can have the probability of every countable
> set equal to zero and still have meaningful probability. It is only
> spaces of countable cardinality that cause this sort of trouble if one
> wishes sets of equal cardinality all to have the same probability.

Did anyone say anything about wishing sets of equal cardinality all to
have the same probability? Is that what the OP was talking about? I
didn't try to read his post, as it seemed kind of obscure. Of course
it's not possible, in an infinite sample space, for sets of the same
cardinality all to have the same probability. (I'm assuming the axiom
of choice, so I don't have to worry about Dedekind-finite infinite
sets.)

Date Subject Author
12/20/12 ross.finlayson@gmail.com
12/21/12 FredJeffries@gmail.com
12/21/12 Bill Taylor
12/22/12 Porky Pig Jr
12/22/12 ross.finlayson@gmail.com
12/24/12 FredJeffries@gmail.com
12/22/12 David Bernier
12/22/12 Butch Malahide
12/24/12 FredJeffries@gmail.com
12/24/12 Butch Malahide
12/25/12 Virgil
12/25/12 Butch Malahide
12/25/12 Virgil
12/25/12 Butch Malahide
12/25/12 Virgil
12/25/12 Butch Malahide
12/26/12 gus gassmann
12/26/12 Butch Malahide
12/27/12 ross.finlayson@gmail.com
12/27/12 ross.finlayson@gmail.com
12/28/12 Virgil
12/28/12 ross.finlayson@gmail.com
12/28/12 Virgil
12/28/12 ross.finlayson@gmail.com
12/28/12 Virgil
12/28/12 ross.finlayson@gmail.com
12/25/12 Shmuel (Seymour J.) Metz
12/25/12 Butch Malahide