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Probability Distribution Function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg125172] Probability Distribution Function
*From*: Niles <niels.martinsen at gmail.com>
*Date*: Sun, 26 Feb 2012 04:18:52 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
Hi
I have a probablity distribution (Maxwell-Boltzmann) giving the
probability of a classical particle having some velocity v. Now, what
I have is a function to calculate the trajectory for a particle with
some velocity v_i. I need to apply this function to the whole
distribution. My question is regarding how I should do this.
Originally what I had thought about doing is to partition the
distribution into N small bins, and associate a velocity to each bin.
My plan was then to calculate the trajectory for each velocity (=
bin), and the "output-velocity" I weigh with the original probability/
weight.
1) My first question is if this is a correct method I am using?
2) I have already implemented this is Mathematica. However, for some
distinct bins some of the "output"-velocities are the same. So I need
to figure out some way to add them up, which I don't find that easy.
My problem is to determine how close two data points have to be in
order to be binned together.
Best regards,
Niles.
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