A disclaimer follows:
I offer these questions as a self-test of one's knowledge in particle physics. I am not part of the INFN selection committee. I have no connection to the selection committee, nor any insider information on how the exam will be structured. All I know about it is what is contained in the official call, available to everybody. I do have some previous experience with INFN selections of researchers, but this needs not be relevant for this year's selection.
That said, here is a question that requires a little knowledge of statistics.
1) You have 1 gram of a unknown radioactive element, and you start the clock and detect decays with a counter with zero background. After 1' you observe that 100 decays have been recorded. With that information can you estimate the lifetime of the substance ? Please provide a yes or no answer, and explanation of reasoning.
2) You perform a second counting for the second minute, consecutive after the first. You record 20 decays. How do you do estimate the lifetime now ? We are not interested in the numerical answer, only in the procedure.
3) In light of the magnitude of the above two measurements, what would you give as an estimate of the standard deviation of the first count, i.e. 100 ? Please explain the procedure.
Please provide your answers in the comments thread, so that we can discuss it!!