My Math Forum Linear birth and death process

 November 13th, 2016, 05:34 AM #1 Senior Member   Joined: Feb 2015 From: london Posts: 121 Thanks: 0 Linear birth and death process X(t) - Is the number of people at time t >= 0, which is modelled by a linear birth and death process y - birth rate u - death rate X(0) = a - Initial population size $\displaystyle q(t) = P(X(t) = 0 | X(0) = 1)$ $\displaystyle q_j(t) = P(X(t) = 0|X(0) = j)$ How can I prove that $\displaystyle q_j(t) = (q(t))^j$, j>=2
 November 13th, 2016, 01:26 PM #2 Global Moderator   Joined: May 2007 Posts: 6,510 Thanks: 584 Look at the problem as j independent events, so you can use product rule for probabilities of independent random variables.

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