re: 3 — to be more precise, one can show that $\prod_i (1 - p_i) > 0$ iff $\sum p_i < ∞$, where $p_i \in [0, 1)$ is a probability of extinction in a given year.
Should that be ∑ilog(1−pi)>−∞? Just taking logarithms.
This is a valid convergence test. But I think it’s easier to reason about \sum p_i < ∞. See math.SE for a proof.
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re: 3 — to be more precise, one can show that $\prod_i (1 - p_i) > 0$ iff $\sum p_i < ∞$, where $p_i \in [0, 1)$ is a probability of extinction in a given year.
Should that be ∑ilog(1−pi)>−∞? Just taking logarithms.
This is a valid convergence test. But I think it’s easier to reason about \sum p_i < ∞. See math.SE for a proof.