User:IssaRice/Exponential distribution

this is the only derivation that makes any sense to me (assuming you already understand the poisson distribution): https://neurophysics.ucsd.edu/courses/physics_171/exponential.pdf

this post has a similar derivation, but it is sloppier: http://www.clayford.net/statistics/deriving-the-exponential-distribution/ (e.g. it doesn't do $f(w)=\lambda e^{-\lambda w}$)