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<> = Nk

So this means that if <> = 1 the distribution function must be peaked around 1. In general when is it a good approximation (i.e. when is the function peaked sufficiently narrow) to say that the probability in N tries to have one or more succeses is simply:

P(≥1) = Nk

this obviously does not hold for Nk>1 but on the other hand I don't expect it to hold for small N. So my guess is when Nk is sufficiently small. Is that correct?