A Minimum-variance bound for the extended maximum likelihood estimation

[xxww]

TL;DR

Is there is any limit for the variance of the estimated number in the extended maximum likelihood estimation, like the minimum-variances bound for the parameters in the maximum likelihood?

I am fitting a mass spectrum using pdf(M)=Ns×S(M)+Nb×B(M; a, b) to determine the yield with the extended maximum likelihood fit, where Ns and Nb are the number of signal and background events, S(M) is the function for the signal, B(M;a, b) is the function for the background with parameters a and b.
However, the uncertainty for the Ns in the fit result is smaller than sqrt(Ns). Is it possible to have the uncertainty smaller than that obtained from simple counting? Is there any expectation like the minimum-variance bound for the Ns?

Thanks in advance.

 

[mfb]

However, the uncertainty for the Ns in the fit result is smaller than sqrt(Ns).

Are there any weights on the events? If not that's a strange result.