Poisson Process
Random events in time — the memoryless arrival process
Parameters
Rate λ (events/unit)
3.0
Time window T
10
Realizations
5
Generate
Auto-generate: ON
Poisson process:
P(N(t)=k) = e^(−λt)(λt)^k / k!
Inter-arrival times ~ Exp(λ):
f(x) = λe^(−λx)
Memoryless property:
P(T>s+t|T>s) = P(T>t)
Mean = Var = λt (equidispersion is the hallmark of the Poisson).
Mean count:
—
Var count:
—
λT (theory):
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