# Poisson distribution with efficiency problem

1. Jun 9, 2012

### atomi

Hi,

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?

cheers

2. Jun 9, 2012

### alan2

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.