Empirical probability question: if you have N children what is the expected length L of the longest chain of descendants you might have? Ie how long before your lineage dies out? Make suitable assumptions about distributions of offspring. Feels like a 101 question.
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Here's the set of notes we use in class. Chapter 14 is the one. It's very accessible. https://www.math.ucdavis.edu/~gravner/MAT135A/resources/lecturenotes.pdf …
This MGF trick is adorable! I learned this general fact about composing MGFs ages ago but I think this is the first real application of it I've seen. Can you get a good estimate on the expected # of generations before extinction (in the case that extinction happens a.s.)?
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Right? It's so pleasing! So I just derived this series for the expected lineage length (I think it's right, though I haven't seen it in other places), which is kind of neat. To get simpler estimates you could bound the convergence rate to the extinction fixed point.pic.twitter.com/VTIAMF39ec
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