Hw9_ORIE361_2008

Hw9_ORIE361_2008 - ORIE 361/523 Homework 9 Instructor Mark...

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ORIE 361/523 – Homework 9 Instructor: Mark E. Lewis due April 9, 2008 (drop box) 1. Each individual in a biological population is assumed to give birth at an exponential rate λ and to die at an exponential rate μ . In addition, there is an exponential rate of increase θ due to immigration. However, immigration is not allowed when the population size is N or larger. Set this up as a birth and death model. 2. Markov Branching Process. If a given particle is alive at a certain time, its additional life length is a random variable which is exponentially distributed with parameter α . Upon death, it leaves k oﬀspring with probability p k ,k 0 . As usual, particles act independently of other particles and of the history of the process. For simplicity, assume p 1 = 0. Let X ( t ) be the number in the population at time t . Find the generator matrix( S (State Space) = { 0 , 1 , 2 , ···} ). 3.

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This note was uploaded on 03/01/2010 for the course ORIE 361 taught by Professor Lewis,m. during the Spring '07 term at Cornell.

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Hw9_ORIE361_2008 - ORIE 361/523 Homework 9 Instructor Mark...

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