categories - Category Theory list
 help / color / mirror / Atom feed
From: "David Espinosa" <david@davidespinosa.net>
To: "Categories" <categories@mta.ca>
Subject: Axioms of elementary probability
Date: Fri, 8 May 2009 23:02:04 -0700	[thread overview]
Message-ID: <E1M2mgx-00042j-9H@mailserv.mta.ca> (raw)


Here's a question about elementary (naive, finitist) probability.
The proper, self-dual axioms for elementary probability are presumably

  P(0) = 0
  P(X) = 1
  P(A u B) + P(A n B) = P(A) + P(B)

P's domain is a boolean algebra.  P's codomain is [0,1].
What kind of algebraic structure is [0,1] in this case?

What can we prove from this theory?  The best I can think of is inclusion /
exclusion:

  P(A u B u C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n
B n C)
  P(A n B n C) = P(A) + P(B) + P(C) - P(A u B) - P(A u C) - P(B u C) + P(A u
B u C)

Thanks,

David






             reply	other threads:[~2009-05-09  6:02 UTC|newest]

Thread overview: 7+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2009-05-09  6:02 David Espinosa [this message]
2009-05-12 15:34 ` Steve Vickers
2009-05-12  1:53 Ross Street
2009-05-12 17:52 Jeff Egger
2009-05-13 13:52 RFC Walters
2009-05-13 19:59 Greg Meredith
2009-05-15 19:35 Greg Meredith

Reply instructions:

You may reply publicly to this message via plain-text email
using any one of the following methods:

* Save the following mbox file, import it into your mail client,
  and reply-to-all from there: mbox

  Avoid top-posting and favor interleaved quoting:
  https://en.wikipedia.org/wiki/Posting_style#Interleaved_style

* Reply using the --to, --cc, and --in-reply-to
  switches of git-send-email(1):

  git send-email \
    --in-reply-to=E1M2mgx-00042j-9H@mailserv.mta.ca \
    --to=david@davidespinosa.net \
    --cc=categories@mta.ca \
    /path/to/YOUR_REPLY

  https://kernel.org/pub/software/scm/git/docs/git-send-email.html

* If your mail client supports setting the In-Reply-To header
  via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line before the message body. 
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).