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And "e" Appears from Nowhere: Quick Numerical Experiment with Clojure
- cjg 16y agoThis is the most interesting bit: "Select a random number between 0 and 1. Now select another and add it to the first. Keep doing this, piling on random numbers. How many random numbers, on average, do you need to make the total greater than 1? The answer is e." The proof appears right at the bottom.
- RBerenguel 16y agoAnd the proof is simpler than it would appear from reading the enunciate (at least that's what I think, of course!)
- pjscott 16y agoThat proof is amazingly clever.
- technoguyrob 16y agoCould be an easy Putnam problem.
- Confusion 16y agoI think you are underestimating the complexity of coming up with an analogy that works. For instance, solving the same problem for 'How many numbers are needed to exceed 2' is already much harder and I don't think there exists a similar 'easy' proof.
- RBerenguel 16y agoIt was indeed a Putnam problem. Good guess ;)
- etal 16y agoFor kicks, here it is in R: PlusRandom <- function(initial, steps) { if (initial > 1) steps else PlusRandom(initial + urand(1), steps + 1) } mean(replicate(100000, PlusRandom(0,0)) [1] 2.71872
- Marticus 16y agoI like it, although reading it at 9 AM this morning just hurt until I could think about it in more detail later. Pretty awesome really.