My Math Forum Linear birth and death process

 November 13th, 2016, 06:34 AM #1 Member   Joined: Feb 2015 From: london Posts: 90 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, 02:26 PM #2 Global Moderator   Joined: May 2007 Posts: 6,133 Thanks: 468 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

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post power3173 Advanced Statistics 0 March 5th, 2015 03:09 PM jon90 Linear Algebra 0 April 5th, 2014 11:07 AM westworld Algebra 35 January 31st, 2012 09:34 PM westworld Elementary Math 6 January 25th, 2012 08:46 PM tottijohn Advanced Statistics 0 September 6th, 2011 06:55 AM

 Contact - Home - Forums - Top