The dispersion (standard deviation) of the estimator of neutron flux number

Scatterer

Hello people, I think the problem what I have is well known in experimental physics. Hope, somebody can helps me, thanks in advance. Here is:

There is a source of neutrons with a flux of λ neutrons per minute, which you do not know and want to estimate. You open the detector for one minute and it counts N neutrons. The maximum likelihood estimator for λ would be N.
Find the dispersion (or standard deviation) of this estimator. What will it be for the limiting case N=0?

Looks like Poisson distribution, where λ isn't known.

DrDu

Yes, exactly. What is the standard deviation in terms of lambda for a Poisson distribution?

Scatterer

Standard deviation in terms of lambda is square root from lambda, but my event is different I think, have you any idea?

DrDu

I think this is the best you can get with just one measurement. To estimate an empirical variance would require at least two measurements.