Poisson proces and binomial


TS Contributor
I'm trying to find the distribution of the number \(Y\) of arrivals in the
timeinterval \([s,t]\subset [0,T]\) where X(t) is number of arrivals in a poissonproces and it is given that X(T)=N.

The result I get is that:

\(Y=X(t-s)|X(T)=N\) is binomial \(bin(n,p)\) with n=N and p=|t-s|/T

where \( s < t\) and \([s,t]\subset [0,T]\)

I'm wondering if anyone would happen to know whether this result is correct?