
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
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) $ $\displaystyle q_j(t) = P(X(t) = 0X(0) = j)$ 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: 6,133 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  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
some Markov chain questions in Brownian Motion and BirthDeath  power3173  Advanced Statistics  0  March 5th, 2015 03:09 PM 
Linear Programming to Improve a manufacturing process  jon90  Linear Algebra  0  April 5th, 2014 11:07 AM 
1/29 of the year of birth...  westworld  Algebra  35  January 31st, 2012 09:34 PM 
A man's age is 1/29 of the year of his death...  westworld  Elementary Math  6  January 25th, 2012 08:46 PM 
Continuous Time Markov Chain  ImmigrationBirth Process  tottijohn  Advanced Statistics  0  September 6th, 2011 06:55 AM 