Discussion
Which of the following is true ?
A linear death process is a continuous time Markov chain, where :
Answer: C
In a linear death process, 0 is a non-null persistent state and all other states are transient.
In a linear death process the population of size \(n\) falls to \(n - 1\) at rate \(n\mu\), and there are no births. State 0 is absorbing: once the population dies out it stays at 0 forever. An absorbing state is persistent with mean recurrence time finite (the chain never leaves), so it is non-null persistent.
Every state \(n \ge 1\) is left with certainty and can never be re-entered, because the population only decreases. So every such state is transient. That rules out 'all states non-null persistent', 'all states transient' (0 is not), and 'other states null persistent'.
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