Uncertainty of MonteCarlo Simulations: Weight and Error Bars

[Aleolomorfo]

Hello everybody,
I need a help, primarly a confirmation about my reasoning. I have data from a MonteCarlo simulation of collisions between particles at LHC (made with Madgraph). I have plotted some variables, for example the angle between two final leptons. Then I have normalized the plot to a determined integrated luminosity, so I have applied a weight to the histogram. I'd like to put error bars due to the uncertainty of the generated event from the MonteCarlo, which is a poisson error. So I have taken the content of each bin and then made the square root. But I have some doubt. First of all, shouldn't I take into consideration the weight in some way? Secondly, I'm not so sure about $\sqrt{N}$, because maybe it should be something like $\frac{\sqrt{N}}{N-1}.$
Thanks in advance

 

[mfb]

Are your original events without weights?
In that case the error bars on the original distribution should be sqrt(N). The luminosity is just a constant scaling for both central value and uncertainties (no uncertainty on the luminosity in MC).

If your original events have weights things can get more complicated. Luminosity stays a constant factor, however.

 

[Aleolomorfo]

Yes, my original events are without weights.
Thank you very much for the answer!