5 ms·

I was aware that the Random function call gets evaluated in Python (and C) every time the loop iterates, I just couldn't imagine the probability distribution my

I was aware that the Random function call gets evaluated in Python (and C) every time the loop iterates, I just couldn't imagine the probability distribution myself, I had assumed that all numbers are uniformally distributed but didn't cater for the sums. You're a legend! Now I see it. I wrote the following code to check out your argument and it checks out indeed :thumbs-up: def p(n): total = 1 for i in range(1, n): total *= (100-i)/100 return total for i in range(1, 100): print(f"p({i}) = {p(i)}") The first 13 results: p(1) = 1 p(2) = 0.99 p(3) = 0.9702 p(4) = 0.9410939999999999 p(5) = 0.9034502399999998 p(6) = 0.8582777279999998 p(7) = 0.8067810643199997 p(8) = 0.7503063898175998 p(9) = 0.6902818786321918 p(10) = 0.6281565095552946 p(11) = 0.5653408585997651 p(12) = 0.503153364153791 p(13) = 0.44277496045533604 p(12) sits at 50%, of course it will be the mean! :D

Someone 3y ago
> p(12) sits at 50%, of course it will be the mean! Technically, “the mean is 12” does not follow at all from “p(12) sits at 50%”. “p(12) sits at 50%” implies the median (https://en.wikipedia.org/wiki/Median https://en.wikipedia.org/wiki/Median) is 12, and that can differ from the mean (https://en.wikipedia.org/wiki/Arithmetic_mean https://en.wikipedia.org/wiki/Arithmetic_mean) of the distribution, and the difference can be quite large. For example, if that list were to continue p(13) = 0.44277496045533604 p(14) = 0.44277496045533604 p(15) = 0.44277496045533604 p(16) = 0.44277496045533604 p(17) = 0.44277496045533604 p(18) = 0.44277496045533604 … p(1000) = 0.44277496045533604 P(1001]) = 0 the about 44% that makes it to 13 also will make it to 1000, and the mean value will be a bit more than 442.77496045533604 (the contribution of that 44.2%) If, on the other hand, it were to continue p(13) = 0.44277496045533604 p(14) = 0.0 No result would be higher than 13, and the mean would be lower than 12.

Someone 3y ago

> p(12) sits at 50%, of course it will be the mean! Technically, “the mean is 12” does not follow at all from “p(12) sits at 50%”. “p(12) sits at 50%” implies the median (https://en.wikipedia.org/wiki/Median https://en.wikipedia.org/wiki/Median) is 12, and that can differ from the mean (https://en.wikipedia.org/wiki/Arithmetic_mean https://en.wikipedia.org/wiki/Arithmetic_mean) of the distribution, and the difference can be quite large. For example, if that list were to continue p(13) = 0.44277496045533604 p(14) = 0.44277496045533604 p(15) = 0.44277496045533604 p(16) = 0.44277496045533604 p(17) = 0.44277496045533604 p(18) = 0.44277496045533604 … p(1000) = 0.44277496045533604 P(1001]) = 0 the about 44% that makes it to 13 also will make it to 1000, and the mean value will be a bit more than 442.77496045533604 (the contribution of that 44.2%) If, on the other hand, it were to continue p(13) = 0.44277496045533604 p(14) = 0.0 No result would be higher than 13, and the mean would be lower than 12.