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From: Brown Bannister on 30 Mar 2010 20:53
This problem concerns the expression of N elements with P probability
of change
as the elemments are copied.

1. Begin with N elements and a probability p of change in each
element.
2. The probability each element will not change is 1-p.
3. N x p elements will change in copying elements.
4. N x (1 - p) elements will not change in copying elements.

Example:

1. 10 with a 10% probability of each element being changed.
2. The probability each element will not change is 1 - .1
3. 10 * .1 = 1 element will be changed in copying elements.
4. 10 x (1 - .1) = 9 elements will not be changed in copying elements.

A book is being printed for the first time. The book has 10 chapters.

There is a 10% chance a chapter of the book will change before the
second printing.

One chapter of the second edition differs from the first.
Nine chapters of the second edition are unchanged.

Coram nobis crescit eundo mutatis mutandis.
The error before us grows as it goes by changing those things which
need to be changed.

P Versus NP, the implications of the predictions of a statement apply
to it.
From: Brown Bannister on 30 Mar 2010 21:02
On Mar 30, 5:53 pm, Brown Bannister <brownbannis...(a)beatlesfan.com>
wrote:
> This problem concerns the expression of N elements with P probability
> of change
> as the elemments are copied.
>
> 1. Begin with N elements and a probability p of change in each
> element.
> 2. The probability each element will not change is 1-p.
> 3. N x p elements will change in copying elements.
> 4. N x (1 - p) elements will not change in copying elements.
>
> Example:
>
> 1. 10 with a 10% probability of each element being changed.
> 2. The probability each element will not change is 1 - .1
> 3. 10 * .1 = 1 element will be changed in copying elements.
> 4. 10 x (1 - .1) = 9 elements will not be changed in copying elements.
>
> A book is being printed for the first time. The book has 10 chapters.
>
> There is a 10% chance a chapter of the book will change before the
> second printing.
>
> One chapter of the second edition differs from the first.
> Nine chapters of the second edition are unchanged.
>
> Coram nobis crescit eundo mutatis mutandis.
> The error before us grows as it goes by changing those things which
> need to be changed.
>
> P Versus NP, the implications of the predictions of a statement apply
> to it.

Sum numbers...

N=8 and p=.25

Number of changes Probability of this Probability of at
many changes least this many changes

0 10.0% 10.0%
1 26.7% 36.7%
2 31.1% 67.9%
3 20.8% 88.6%
4 8.7% 97.3%
5 2.3% 99.6%
6 0.4% 100%
7 0.0% 100%
8 0.0% 100%


-BB
From: Paul E. Black on 2 Apr 2010 12:28
On Tuesday 30 March 2010 20:53, Brown Bannister wrote:

> This problem concerns the expression of N elements with P probability
> of change as the elemments are copied.
>
> 1. Begin with N elements and a probability p of change in each element.
....
> 3. N x p elements will change in copying elements.
....
>
> Example:
>
> 1. 10 with a 10% probability of each element being changed.
....
> 3. 10 * .1 = 1 element will be changed in copying elements.
....

The formula 3 is the *expected* number of elements that will change in
copying, assuming independence. If it really is random, all might
change or none might change. This is easier seen. Suppose there are
12 elements each with a 10% probability of being changed. Will 1.2
elements change??

-paul-
--
Paul E. Black (p.black(a)acm.org)
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