Re: [Schematics-development] Schemathics: Documentation of random variables

[Ian G. <ia...@ma...>]

On Tuesday 06 May 2003 17:53, Jens Axel S=F8gaard wrote:
> >(And after all the Dirac delta is a statistical distribution).
>
> I'm not quite sure that's right - a statistical distribution is still a
> function (isn't it?).

Probably not quite expressed correctly, I think I should have said the de=
lta=20
measure is statistical distribution. The idea being that continuous=20
probabilities are defined better by measures than functions. The uniform=20
distribution f(x) =3D 1 for 0 < x < 1, the actual value of the function a=
t=20
point isn't really statistical meaningful only it's integral over subsets=
 of=20
R is - just like the values of delta(x) aren't always meaningful but the=20
integrals are.

> >But then that is maths in a nutshell, "assume this and what interestin=
g
> > things drop out." Though for delta (I'm fairly sure that) you can ass=
ume
> > more fundamental things and it's existence, integrability etc. drops =
out.
>
> It's not just playing with axioms. You can make intermediate (ary?)
> calculations involving delta,
> and in the end all the deltas cancel out, and you are left with an
> ordinary function as a result.
> One can use this to study certain kinds of differential equations.

Agreed.