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Cool. But note that this is not a problem that you're likely to run into in practice. Nolan and Gelman claim that you can't actually bias a coin. http://www.
by cvwright 10y ago
Cool. But note that this is not a problem that you're likely to run into in practice. Nolan and Gelman claim that you can't actually bias a coin.
http://www.stat.berkeley.edu/~nolan/Papers/dice.pdf http://www.stat.berkeley.edu/~nolan/Papers/dice.pdf
- paulgerhardt 10y agoHow to create an unfair coin and prove it with math: https://izbicki.me/blog/how-to-create-an-unfair-coin-and-prove-it-with-math.html https://izbicki.me/blog/how-to-create-an-unfair-coin-and-pro...
- babuskov 10y ago> Amazingly, it takes some pretty big bends to make a biased coin. It’s not until coin 3, which has an almost 90 degree bend that we can say with any confidence that the coin is biased at all. Basically, it proves that creating a biased coin really is impossible.
- andreasvc 10y agoIt is impossible by bending. It's probably still possible (not to say practical) by crafting a coin with a hidden compartment of a heavier metal.
- morinted 10y agoFrom the paper linked above: 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.
- babuskov 10y agoThe paper states that this would only alter the center of mass. If you catch the coin or it lands on a soft surface, it has no effect, because the outcome is determined by the time when it stops. If you allow it to bounce, then yes. TL;DR: if you want unbiased coin IRL, make sure you catch it before it hits the ground.
- j2kun 10y ago"Coin" is a metaphor in mathematics for any process with a binary outcome (a binary random variable, so to speak). These things exist in practice everywhere.