Years ago, Zeev Rudnick defined Poisson generic sequences as those where the number of occurrences of the long strings in the initial segments of the sequences follow the Poisson distribution. Peres and Weiss proved that almost all sequences, with respect to Lebesgue measure, are Poisson generic, but they did not publish their proof. In this note first we transcribe Peres and Weiss' proof and
... [Show full abstract] then we show that there are computable Poisson generic instances and that all Martin-L\"of random sequences are Poisson generic.