note: N(t) is the number of points in [0,t] and N(t1,t2] is the number of points in (t1,t2].(adsbygoogle = window.adsbygoogle || []).push({});

Let {N(t): t≥0} be a Poisson process of rate 1.

Evaluate E[N(3) |N(2),N(1)].

If the question were E[N(3) |N(2)], then I have some idea...

E[N(3) |N(2)]

=E[N(2)+N(2,3] |N(2)]

=E[N(2)|N(2)] + E{N(2,3] |N(2)}

=N(2)+ E{N(2,3]} (independent increments)

=N(2) + 1

since N(2,3] ~ Poisson(1(3-2)) =Poisson(1)

But for E[N(3) |N(2),N(1)], how can I deal with the extra N(1)?

Thanks for any help! :)

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# Poisson process: compute E[N(3) |N(2),N(1)]

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