I found out that Poisson distribution “expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event.” (wiki) I think it may be related to QM.
Anyways, the only parameter λ in the poisson equation is “expected number of occurrences” in a given interval; that is, if λ is set to be 1, the event is expected to happen only one time in a given interval (time/distance/whatever). Because λ is always positive, the poisson equation is always larger than 0, and thus the negative part can be thrown out…(maybe?)
From the wiki, the plot shows that, in the case of λ=1, the probability of the event to occur exactly (shown by the x-axis) is about 0.7 (which is about the same as the plot I got from fitting). [But I don’t fully understand why…] As λ increases, the plot spreads out. (Why? – I am still thinking …)
Anyways, I just share what I know and what I don’t know… If I said something wrong/you know something that I miss, let me know!