This has been done in [this experiment][1] 

>Poisson statistics were studied using the radioactive decay of1 7Cs as a source. A scintillation counter measured gamma rays emitted by 137Cs as well as background from cosmic rays and other experiments in the laboratory. Data from approximate mean rates of 1, 4, 10 and 100 counts/sec was compared to both theoretical Poisson distributions and Monte Carlo simulations. The reduced chi squared values for the fits to theoretical distributions ranged from 0.57 to 2.13. The values from the Monte Carlo simulations were within the margin of statistical error of the data. Thus, it was found that gamma rays from the radioactive decay of Cs with added background events is accurately modeled by Poisson statistics, *so each decay event in a bulk source is a random, independent event*.

Italics mine. 

The d[ecay rate curves][2] for radioactive elements are what is useful for experiments,it gives how much the sample is depleted.


  [1]: https://www.semanticscholar.org/paper/Poisson-Statistics-of-Radioactive-Decay-Campbell-Duarte/36db50355116e6e5feea4155ea60077e9fa5ad40
  [2]: http://www.splung.com/content/sid/5/page/radioactivity