I also have a one-line solution for the Forsythe’s method! Soon to be posted on the ‘Og, but already updated within my resolution on X validated.

]]>True. This is a rank property.

]]>This is very concise indeed. I am seeking a similar line for the Gnedenko solution, aiming at analysing a long uniform vector in one go with no recursion.

]]>Very nice and intuitive explanation as to why the probability is 1/k!

]]>Right! The Glynn-Rhee approach has indeed the power to turn it into an unbiased estimator. Thanks.

]]>One can also think about it in terms of random truncations (a.k.a.Russian roulette). Indeed, an unbiased estimate of “e” is given by the sum from k=1 to k=N of 1/[k! * P(k <= N)] where N is any reasonable integer valued random variable.

If N is the number of uniform random variables one needs to add up to exceed 1 then one precisely has that P(k <= N) = 1/k! and this gives back the mentioned result. But there are many other choices…

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