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November 13th, 2016, 06:34 AM  #1 
Member Joined: Feb 2015 From: london Posts: 98 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) $ $\displaystyle q_j(t) = P(X(t) = 0X(0) = j)$ How can I prove that $\displaystyle q_j(t) = (q(t))^j $, j>=2 
November 13th, 2016, 02:26 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,181 Thanks: 479 
Look at the problem as j independent events, so you can use product rule for probabilities of independent random variables.


Tags 
backward, birth, death, equations, kolmogorov, linear, process 
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