For anyone who cares and read this far (and if so, I'm honestly surprised) I made a colab that demonstrates all this: https://colab.research.google.com/drive/1x

For anyone who cares and read this far (and if so, I'm honestly surprised) I made a colab that demonstrates all this: https://colab.research.google.com/drive/1xCZ24cLPNOqyJD0kUTOUMKm3jDsDb48-?usp=sharing https://colab.research.google.com/drive/1xCZ24cLPNOqyJD0kUTO... To wrap it up: - X == r() * r() * ... == r(r(...)) - E[X] = 2^-n - median[X] ~ 1/2 exp(1 - n) ?! Anyway, I thought it was interesting - especially how the median never quite "catches up" to the value one might naively compute from the CLT. I think there's some subtlety I'm missing there.