Poisson distribution derivation. Intuitive example.

How to know what distribution one should apply when faced with a certain statistical problem ? One way is to know basic examples for when different distributions naturally arise. Here we discuss such an example for Poisson events.

[amiralimoradmand]

That was a true example of connecting provable formulas to intuition.
Nice job man. keep it going

[aidosmaulsharif]

Man you are awesome!! That was a great derivation of poisson distribution without any introduction of binomial distribution. You basically derived exponential from minimum set of assumptions and that's always beautiful to watch. Thanks

This was ridicolously helpful compared to classic way of "teaching" calculus where you are Just exposed to formulas that are completely out of the blue. Thank you so much

[ayyubshaffy]

for the generalization, how do we prove that : N x (N-1) x (N-k+1) / (n-k) approaches--> mean ^ k as N --> infinity . anyways love the take on this proof.

[bahayesilyurt]

thank you a lot for the exquisite explanation

[jonmoore]

Very good, but can you carry it out for k berries, I tried, but not getting it.

[Zero-tgdc]

I have a question about your first example. Since the berries are indistinguishable, surely there would be less than 12^N combinations, since swapping two berries would count as the same combination? I thought you would need to use the stars and bars method so I got (N+11)C(11) different combinations. Am I mistaken that distributions are the same as combinations?