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.