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Topic: function of uniform probability
Replies: 4   Last Post: Feb 11, 2009 3:05 AM

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 Boris Posts: 13 Registered: 12/7/04
Re: function of uniform probability
Posted: Feb 11, 2009 3:05 AM

Matt a écrit :
> On Feb 10, 3:21 pm, Boris Gourévitch <bo...@SUS-AU-SPAMpi314.net>
> wrote:

>
>> I'm working in signal processing and I would like to build a function
>> f(t) (t is time) defined on R+, bounded on [a,b], derivable

>
> I'm wondering if you might mean "differentiable" rather than
> "derivable"...
>

yes, sorry, typical french mistake... ;-)

>> and which
>> verifies Probability(f(t) is in [c,d])=(d-c), [c,d] being included in
>> [a,b].

>
> Do you mean f(t) at a uniformly randomly chosen instant in time? I'm
> not sure it's logically possible to choose such an instant unless you
> constrain t to lie in a finite time interval -- though you can
> sidestep this issue by using a periodic function. Also, probability is
> a number between zero and one, so I'm wondering if you mean the
> probability is *proportional* to d - c, rather than equal to it.
>

yes, you're right, I was too quick, the probability should be proportional.
I guess that another way to express it correctly is: the distribution
function of f(t) is a uniform distribution on [a,b].

Maybe a more rigorous way to present the problem is:
is there a stochastic process Xt, t in R+ (resp. N), differentiable
(resp. with a low pass spectrum) and so that the probability density
function of Xt is uniform ? (A Brownian process is continuous and
follows a gaussian distribution if I remember)

Intuitively, I'm looking for a curve that would freely move with time
between a and b and whose distribution on [a,b] would be uniform.