§ Poisson distribution
- Think about flipping a biased coin with some bias to associate a coin flip to each real number. Call this .
- Define the count of an interval as .
- Suppose that this value is finite for any bounded interval.
- Then the process we have is a poisson process.
- Since the coin flips are independent, all 'hits' of the event must be independent.
- Since there is either a coin flip or there is not, at most one 'hit' of the event can happen at any moment in time.
- Since the bias of the coin is fixed, the rate at which we see s is overall constant.