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Subject: Re: [boost] different matrix library?
From: Edward Grace (ej.grace_at_[hidden])
Date: 20090818 16:12:17
On 18 Aug 2009, at 20:46, joel wrote:
> Edward Grace wrote:
>> No, it's more subtle than that. Almost all of the time there will be
>> a difference between A and B, however this difference is just 'noise'
>> around zero. In order for there to be a meaningful difference the
>> natural random variations of the differences should be significantly
>> different from zero.
> What's the difference between this and "most of the time A and B go at
> the same speed" ?
> apologize my stats ignorance :)
No problem.
You are (I think) confusing probability and probability density.
If  for the sake of argument and to keep the maths easy  you assume
that A and B are both continuous and normally distributed then so
will their difference. [In practice neither of these assumptions are
true but it doesn't change the basic point.]
This normal distribution of the differences will be normal too. This
distribution is a probability density  to obtain a probability you
must integrate it over a region (dT).
http://en.wikipedia.org/wiki/Probability_density_function
If that region has zero width then the probability will also be
zero. Therefore, the probability that you observe A and B going at
the same speed (AB == 0) is zero.
In other words, paraphrasing your comment,
"All of the time you will observe A and B do not go at the same
speed." [*]
That difference however can be an illusion (purely the result of
chance).
ed
[*] Due to the assumptions above being incorrect this may not be true
 the discrete nature of the distribution can lead to differences
that are exactly zero.

"No more boom and bust."  Dr. J. G. Brown, 1997
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