Consider the following population dynamics: at each unit of time, each individua

Question

Consider the following population dynamics: at each unit of time, each individual currently in the population dies with probability p. Also each unit of time, a Possion (a) number of new individuals join the population, the probability of K additional individuals equals a^ke^(-a)/k!. (a)For which value of a is the chain positive recurrent? (b)In these case when the chain is positive recurrent, what is the expected amount of time, if the population begins with zero individuals, until the next time when the population contains no individuals.

Explanation / Answer

Consider the following population dynamics: at each unit of time, each individual currently in the population dies with probability p. Also each unit of time, a Possion (a) number of new individuals join the population, the probability of K additional individuals equals a^ke^(-a)/k!. (a)For which value of a is the chain positive recurrent? (b)In these case when the chain is positive recurrent, what is the expected amount of time, if the population begins with zero individuals, until the next time when the population contains no individuals.

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