I have done a laboratory session at my university where I had to check that the disintegration of nucleii follows a Poisson distribution
where $P(n)$ is the probability of the disintegration of exactly $n$ nuclei for a given time interval.
I measured the data using a computer program and I've been analyzing the data using MatLab but I don't know if the results that I get make sense or not.
The activity of the test sample was $3$ disintegrations per second and when analyzing the data that I got manually I get that it fits via a Poisson distribution of $\lambda=3.45$ but when using the data that I got via the computer I get $\lambda \approx 900$. I believe that this is an error in my calculations.
This leaded me to wonder what is the exact meaning of $\lambda$ in that expression. I understand that it is the mean number of nuclei disintegrated in a given time, but, does that mean that it depends on the size of the sample? What is the meaning of this parameter?