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Poisson distribution with efficiency problem

  1. Jun 9, 2012 #1

    I have a problem with determining the probability distribution function of the number n of detector counts in a given time t. I am assuming the events follow exponential distribution ε(t,λ) = λexp(-λt). Now if that was everything it would simply be a Poisson distribution, however, what I need to acount for is the detector efficiency α (0-1) and I can't think of a way how to do it. Could anyone give me a hint?

  2. jcsd
  3. Jun 9, 2012 #2
    Is the efficiency a known constant? If so, then you just have a multiplicative constant because P(detection/occurrence) = constant. Then the number of occurrences and the corresponding rate are scaled by the efficiency. If it's not a known constant then I would think that it must be determined. If the efficiency is a function of n and t then I would have to think about it.
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