Birth Process Question

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!

score 2 · Accepted Answer · answered Apr 05 '11 at 03:46

2

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

answered Apr 05 '11 at 03:46

Nate Eldredge

97,710

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 05 '11 at 03:47
Why downvote this? – Did Nov 19 '11 at 18:42

Birth Process Question

1 Answers1