How to determine this unknown Prior probability ?


New Member
I'm working on a particle detector for counting the number of a particle beam into a target, for special reason the beam cannot be detected derectly, i have to develop an indirect measurement, that is, using a detector to count partial scattering particles from a beam-intercepting foil, and use the detected number to infer the incident number of the primary beam. Say, when the parimary beam number is N, the scattering number to be detected is a random variable n, following a Gassian distribution.
But in a practical process, only the detected number of scatterred particles is known, i need to find out for a detected number n, how much is the number of parimary particles delivered to the foil ? From Bayes formula, i have f(N|n)=f(N)f(n|N)/f(n), here f(n|N) is known, but how can i determine the form of f(N) and f(n) ? the prior possibility f(N) seems difficult to be determined ?
Any ideas would be appreciated!