Timeline for Meaningful interpretation for fixed point of a probability generating function
Current License: CC BY-SA 4.0
29 events
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| Oct 7 at 23:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 4 at 1:25 | comment | added | JasTonAChair | I'm a bit late to the party, but this resource is very helpful - stats.libretexts.org/Bookshelves/Probability_Theory/…. The key insight is that the probability of extinction $q$ for each generation is greater than the last, but less than 1, so $q_n \to q $ as $n \to \infty $. | |
| Jun 9 at 23:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
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| Nov 3, 2019 at 14:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jul 6, 2019 at 18:40 | review | Close votes | |||
| Jul 14, 2019 at 3:05 | |||||
| Jul 6, 2019 at 18:31 | comment | added | Kostya_I | If $p$ is the extinction probability and the first individual has $n$ children, then the conditional extinction probability is $p^n$. Therefore, $p=\mathbb{E}[p^n]$. With a proof that simple, what more intuition are you asking for? | |
| Jul 6, 2019 at 14:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 8, 2019 at 14:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 6, 2019 at 13:18 | answer | added | Dieter Kadelka | timeline score: 0 | |
| Feb 6, 2019 at 11:59 | comment | added | Dieter Kadelka | Please omit the last two sentences in my first comment. You asked for the implications of $f(s) = s$ for some (not all) $0 < s < 1$. | |
| Feb 6, 2019 at 11:29 | comment | added | Dieter Kadelka | As far as I know generating functions are defined as $f(s) = \mathbb{E}s^X$ for random variables $X$ (often with values in $\mathbb{N}_0$). What is the random variable $X$ in your case? Then $f(s) = s$ implies that $\mathbb{P}(X = 1) = 1$. Is this what you want? | |
| S Feb 5, 2019 at 22:31 | history | suggested | Amir Sagiv | CC BY-SA 4.0 |
tag + link + typo
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| Feb 5, 2019 at 22:06 | review | Suggested edits | |||
| S Feb 5, 2019 at 22:31 | |||||
| Feb 5, 2019 at 21:59 | history | edited | libby | CC BY-SA 4.0 |
added 196 characters in body
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| Feb 5, 2019 at 21:55 | review | First posts | |||
| Feb 5, 2019 at 22:06 | |||||
| Feb 5, 2019 at 21:54 | history | asked | libby | CC BY-SA 4.0 |