Reminds me of the Von Neumann method of using a biased coin to generate unbiased random coin flips: http://web.eecs.umich.edu/~qstout/abs/AnnProb84.html
(Edit: not the algo itself, just the notion of combining randomness.)
(Edit: not the algo itself, just the notion of combining randomness.)
Interestingly the prof emailed me the next semester because that had caught his attention and he had worked out that the two processes are ultimately identical, just using very different notations.
For those of us who don't know systems theory, is there a simpler explanation of this? It sounds interesting
However, their Laplace transforms are much easier: X(s) and R(s), and because of how Laplace transforms work, F(s)X(s) (convolution becomes multiplication after a Laplace transform). So if F(s) is 1 / R(s), F(s)X(s) = X(s) / R(s), which means all of the correlation in X(s) is divided out, and you're left with an uncorrelated function, or fair coin in this case.
Basically, it proves that creating a biased coin really is impossible.
one cannot, for example, weight a coin so that it is substantially more likely to land “heads” than “tails” when flipped and caught in the hand in the usual manner. Coin tosses can be biased only if the coin is allowed to bounce or be spun rather than simply flipped in the air.
TL;DR: if you want unbiased coin IRL, make sure you catch it before it hits the ground.