Radioactive Decay - Gaussian or Poisson

[binbagsss]

Radioactive Decay Probability?

Say you are counting the number of decays and the time of observation is varied. I know that as time increases, the Gaussian Distribution becomes a closer fit to the observed probability than when the time interval takes smaller values because the mean count rate increases, but which is the better fit - Poisson or Gaussian?

I expect Poisson disttribution to remain the better fit throughout, as in this situation the Gaussian distribution can be derived from the Poisson?

Thanks

 

[haruspex]

Yes, the Poisson will always be the exact fit for this. The Gaussian will never give the right shape for very few events.