Timeline for Why does the number of continuous uniform variables on (0,1) needed for their sum to exceed one have mean $e$?
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9 events
| when toggle format | what | by | license | comment | |
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| Mar 12 at 1:51 | comment | added | Henry | @simran There are $n!$ ways of ordering $n$ numbers; if there are no ties (a tie has probability $0$ here) then just one has them in increasing order. $\Pr(Y>n)=\frac 1{n!}$ is the probability of not having exceeded $1$ in the first $n$ attempts so gives the complementary CDF. | |
| Jul 29, 2021 at 4:06 | comment | added | simran | and if sum of $ \ X_i $ is supposed to exceed 1 then why do we have less that sign in 3rd last equation ?? | |
| Jul 29, 2021 at 4:01 | comment | added | simran | Can anyone explain why is it that "There is exactly one sequence in which the Ui are already in increasing order, " ?? | |
| Feb 8, 2016 at 14:58 | comment | added | Xi'an | I am referring to your Poisson process simulation via the uniform spacing, in the thread Approximate e using Monte Carlo Simulation for which I cannot get a full derivation. | |
| Feb 8, 2016 at 13:21 | comment | added | whuber♦ | @Xi'an Could you indicate more specifically what you mean by "uniform spacings" in this context? | |
| Feb 8, 2016 at 12:15 | comment | added | Xi'an | And could you add the proof with the uniform spacings as well? | |
| Feb 7, 2016 at 4:52 | comment | added | Antoni Parellada | here and here. | |
| Feb 7, 2016 at 2:04 | comment | added | Antoni Parellada | I have read it a couple of times, and I almost get it... I posted a couple of questions in the Mathematics SE as a result of the $e$ constant computer simulation. I don't know if you saw them. One of them came back before your kind explanation on Tenfold about the ceiling function of the $1/U(0,1)$ and the Taylor series. The second one was exactly about this topic, never got a response, until now... | |
| Feb 7, 2016 at 1:01 | history | answered | whuber♦ | CC BY-SA 3.0 |