# Is this variable following a poisson distribution or a binomial distribution?

##### New Member
You're at a bus stop watching people go by, not buses.
Let X = number of people wearing headphones

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#### rogojel

##### TS Contributor
hi,
you would need to define some limit I guess - say X - the number of people wearing headphones out of 100 observed passangers. If you can assume that during the observation period the probability of wearing headphones is roughly constant then it should be pretty much a binomial. If this is not the case then maybe a mixture of several binomials wiith different ps?

As the Poisson is related to the Binomial, it might happen that a Poisson could also be a good model (if you are observing a LOT of passengers and they generally have a low probability of wearing headphones.

http://www.the-idea-shop.com/article/216/deriving-the-poisson-distribution-from-the-binomial

regards