# Birth Process Question

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

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 $P(X(5)=x)$?