Poisson process

A process of arrivals in continuous time is called a Poisson process with rate $𝜆$ iff both of the following conditions holds:

The number of arrivals in an interval of length $𝑡$ is distributed according to the Poisson distribution $P o i s (𝜆 𝑡)$
The number of arrivals that occur in disjoint intervals are independent of each other

It follows that the number of arrivals in an interval of length 1 is distributed according to $P o i s (𝜆)$ and the time between arrivals are independently distributed according to the exponential distribution $E x p (𝜆)$ . #m/thm/prob

Proof

#missing/proof

warning

This can be generalized

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