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Conditioning a Poisson Arrival Process

Consider a Poisson process with parameter  \(\lambda\). What is the conditional probability that \(N(1) = n\) given that \(N(3) = n\)? (Here, \(N(t) \) is the number of calls which arrive between time 0 and time \(t\). ) Do you understand why this probability does not depend on \(\lambda\)?

 

[Meester ex 7.5.4]

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