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The Yule process is a pure birth process with parameter $\lambda_n = n\beta$. If $X(0) = 1$, then find the probability there are no births during the time interval $(5,8]$.

I was thinking of conditioning on $X(5)$ but I was unsure on how to proceed… Thanks for the help!

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Care to accept an answer? – Did Nov 13 '11 at 10:18
up vote 1 down vote accepted

Conditioning sounds like a good idea. If we call $A$ the event of no births in $[5,8)$, can you find $P(A | X(5) = x)$? And can you find $P(X(5)=x)$?

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Can we more concretely represent A in terms of X(t)? Would P(X(5) = x) just be Poisson? I'm still not sure what to do :S Thanks for the help! – icobes Apr 5 '11 at 3:47
Why downvote this? – Did Nov 19 '11 at 18:42

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