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Re: Testing random

From Jussi Piitulainen <jpiitula@ling.helsinki.fi>
Newsgroups comp.lang.python
Subject Re: Testing random
Date 2015-06-17 07:41 +0300
Organization A noiseless patient Spider
Message-ID <lf5k2v3ymj3.fsf@ling.helsinki.fi> (permalink)
References (4 earlier) <mailman.257.1433694323.13271.python-list@python.org> <1656356.OjxBvjpJ5d@PointedEars.de> <mailman.259.1433695485.13271.python-list@python.org> <5515034.V7dcXEWAvK@PointedEars.de> <88ba163e-74f4-40fa-ab3e-1feeb051b961@googlegroups.com>

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Ned Batchelder writes:

> Thomas: let's say I generate streams of N digits drawn randomly from
> 0-9.  I then consider the probability of a zero *never appearing once*
> in my stream.  Let's call that P(N).  Do you agree that as N
> increases, P(N) decreases?

In probability theory, that could be phrased as the probability that N
unknown digits d_1, ..., d_N are all positive, assuming the digits are
independent (so learning one digit doesn't reveal anything about any
other digit), and for each d_k, the probability p_k of having a positive
digit is the same. Mathematicians often abbreviate these assumptions as
"i.i.d" for "independent" and "identically distributed".

Also assuming uniform distributions, p_1 = p_2 = ... = p_N = 9/10.

P(d_k > 0 for k = 1, ..., N) =
P(d_1 > 0 and d_2 > 0 and ... and d_N > 0) = (by independence)
P(d_1 > 0) * P(d_2 > 0) * ... * P(d_N > 0) =
p_1 * p_2 * ... * p_N = (by identical uniform distribution)
(9/10)^N

In mathematics, (9/10)^N decreases as N increases, so one should indeed
agree. Using more impressive notation and terminology correctly will not
change the analysis.

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Thread

Testing random Cecil Westerhof <Cecil@decebal.nl> - 2015-06-07 08:27 +0200
  Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 12:40 +0200
    Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-07 21:51 +1000
      Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 17:51 +0200
        Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 02:25 +1000
          Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 18:36 +0200
            Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 02:44 +1000
              Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 20:23 +0200
                Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 04:52 +1000
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 21:41 +0200
                Re: Testing random Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2015-06-07 22:08 +0300
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 21:29 +0200
                Re: Testing random random832@fastmail.us - 2015-06-07 15:44 -0400
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 22:09 +0200
                Re: Testing random random832@fastmail.us - 2015-06-07 16:41 -0400
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 22:59 +0200
                Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-08 11:26 +1000
                Re: Testing random random832@fastmail.us - 2015-06-07 21:34 -0400
                Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 11:42 +1000
                Re: Testing random MRAB <python@mrabarnett.plus.com> - 2015-06-08 02:49 +0100
                Re: Testing random random832@fastmail.us - 2015-06-07 21:57 -0400
                Re: Testing random Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2015-06-08 10:40 +0300
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-10 19:03 +0200
                Re: Testing random sohcahtoa82@gmail.com - 2015-06-10 10:52 -0700
                Re: Testing random Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2015-06-10 23:00 +0300
                Re: Testing random Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-10 12:02 -0600
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-12 23:32 +0200
                Re: Testing random alister <alister.nospam.ware@ntlworld.com> - 2015-06-12 21:46 +0000
                Re: Testing random random832@fastmail.us - 2015-06-12 17:52 -0400
                Re: Testing random Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-12 16:00 -0600
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-13 00:09 +0200
                Re: Testing random sohcahtoa82@gmail.com - 2015-06-12 15:55 -0700
                Re: Testing random random832@fastmail.us - 2015-06-12 18:57 -0400
                Re: Testing random Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-06-13 08:53 +0100
                Re: Testing random random832@fastmail.us - 2015-06-10 14:26 -0400
                Re: Testing random Ned Batchelder <ned@nedbatchelder.com> - 2015-06-07 14:21 -0700
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-16 21:18 +0200
                Re: Testing random random832@fastmail.us - 2015-06-16 16:23 -0400
                Re: Testing random Ned Batchelder <ned@nedbatchelder.com> - 2015-06-16 13:48 -0700
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-16 23:57 +0200
                Re: Testing random sohcahtoa82@gmail.com - 2015-06-16 15:30 -0700
                Re: Testing random Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-16 16:58 -0600
                Re: Testing random Laura Creighton <lac@openend.se> - 2015-06-17 11:28 +0200
                Re: Testing random Ned Batchelder <ned@nedbatchelder.com> - 2015-06-16 16:26 -0700
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-17 01:45 +0200
                Re: Testing random sohcahtoa82@gmail.com - 2015-06-16 17:36 -0700
                Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-17 11:01 +1000
                Re: Testing random Ethan Furman <ethan@stoneleaf.us> - 2015-06-16 18:32 -0700
                Re: Testing random Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-06-17 09:41 +0100
                Re: Testing random Grant Edwards <invalid@invalid.invalid> - 2015-06-17 14:04 +0000
                Re: Testing random Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-17 09:01 -0600
                Re: Testing random MRAB <python@mrabarnett.plus.com> - 2015-06-17 01:42 +0100
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-17 08:53 +0200
                Re: Testing random Christian Gollwitzer <auriocus@gmx.de> - 2015-06-17 09:22 +0200
                Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-17 17:28 +1000
                Re: Testing random Tim Golden <mail@timgolden.me.uk> - 2015-06-17 08:30 +0100
                Re: Testing random Cecil Westerhof <Cecil@decebal.nl> - 2015-06-17 11:57 +0200
                Re: Testing random Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-06-17 01:36 +0000
                Re: Testing random Laura Creighton <lac@openend.se> - 2015-06-17 12:33 +0200
                Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-17 22:47 +1000
                Re: Testing random Laura Creighton <lac@openend.se> - 2015-06-17 15:50 +0200
                Re: Testing random Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-06-17 01:35 +0000
                Re: Testing random Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2015-06-17 07:41 +0300
                Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-08 11:11 +1000
            Re: Testing random Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-07 11:07 -0600
            Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 03:20 +1000
            Re: Testing random "C.D. Reimer" <chris@cdreimer.com> - 2015-06-07 10:36 -0700
            Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-08 04:28 +1000
              Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 04:40 +1000
        Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-08 04:24 +1000
  Re: Testing random Jonas Wielicki <jonas@wielicki.name> - 2015-06-07 12:41 +0200
  Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-07 22:52 +1000
    Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-07 23:06 +1000
    Re: Testing random Peter Otten <__peter__@web.de> - 2015-06-07 15:35 +0200
      Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 18:36 +0200
        Re: Testing random Peter Otten <__peter__@web.de> - 2015-06-07 18:48 +0200
          Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 22:15 +0200
      Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-08 11:35 +1000
  Re: Testing random Christian Gollwitzer <auriocus@gmx.de> - 2015-06-07 14:53 +0200
  Re: Testing random Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2015-06-07 11:04 -0400

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