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I have a problem with determining the probability distribution function of the numbernof detector counts in a given timet. 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?

cheers

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# Poisson distribution with efficiency problem

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