# Probability distributions and particles

1. Feb 25, 2012

### Niles

Hi

My question is not related to a specific piece of software, but more of a technique. I have a probablity distribution 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 vi. I need to apply this function to the whole distribution. My question is 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.

Last edited: Feb 25, 2012
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