Q: Most Likely!

Discussion in 'Probability' started by Geoff Jones, Jul 7, 2004.

  1. Geoff Jones

    Geoff Jones Guest

    Hi

    I was wondering if anybody could give me some thoughts on the following
    problem:

    Suppose we have two radioactive particles which emit particles at a given
    rate. Suppose also that we have two Geiger counters a certain distance from
    both particles. Let us denote the "strength" of the particles by Si (where i
    is an index for the particle). Let us also denote the distance of the Geiger
    counter j to the particle i as Dij. Suppose also that the probability of a
    counter receiving a "hit" from particle i is inversely proportional to the
    distance from it.

    If one of the Geiger counters records a "hit" from one of the radioactive
    sources, how do we work out which one is the most likely one?

    Thanks in advance

    Geoff
     
    Geoff Jones, Jul 7, 2004
    #1
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  2. Geoff Jones

    jeffc Guest

    It totally depends on how the distance affects the result and how the
    strength affects the result. It's kind of arbitrary without that knowledge.
    But basically the probability of a hit from particle i is going to be
    proportional to the strength and inversely proportional to the distance.
    Like P(i) is Si/Dij, with some extra stuff thrown in to make the 2
    probabilities add up to 1.
     
    jeffc, Jul 13, 2004
    #2
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