# Multiplicity Smearing

+ ### The original concept:
> Let me follow the original one first, where they try to smear the gen lvl multiplicity to the reco lvl distribution.

1. Given a certain response matrix, will have the gen lvl mult ($x$) smear to the corresponded reco lvl distribution ($N(y)|_{x}$)
2. So the concept is actually like a convolutional operation: $\delta(x) \to f(y)|_{x}$ ($f(y)|_{x}$: normalized $N(y)|_{x}$), for instance:
for $N_{trk}^{gen}=8$, after the operation, will become a smeared distribution
3. This can make the smeared gen ntrk distribution look like reco's:
4. This will not ensure the event-to-event matching btw reco, gen mult, since when doing the smearing as point 2 suggests, it is a random-sampling process.

+ ### Conclusion:
It seems to me that this is an operation only applicable on gen level, where we do want smeared/randomized the gen distribution

+ ### Detailed results:
https://drive.google.com/drive/folders/1pOr61WhGcglmqP3o5HyS1sCPbaoezMpk?usp=sharing