Poisson distribution

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 Pois(𝜆𝑡)
• 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 Pois(𝜆) and the time between arrivals are independently distributed according to the exponential distribution Exp⁡(𝜆). prob

Proof

proof

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