1. The problem statement, all variables and given/known data I am given a table of ~3000 measurements for the number of decays from some radioactive substance within some period T. I want to estimate the mean number of decays per period. 2. Relevant equations Poisson distribution How to calculate mean. 3. The attempt at a solution My intuition tells me that the best estimator is simply the to take the arithmetic mean of the dataset. However, given that the data should follow a poisson distribution I am not sure. When is the arithmetic mean the best estimator, and if this is indeed the case, why is it superior to for example fitting to a poisson distribution and then reading of the mean from the fit coefficients?