The coin flip is a brilliant piece of technology for generating trustworthy random noise:
Making a two-headed coin is forgery, which is a crime.
Such trick coins can be foiled anyways by calling the toss in the air.
Thus when teaching the concept of a Bernoulli variable, we use the example of coin flips, because everyone already knows what they are. This is unfortunate because the very next concept we introduce is a biased Bernoulli variable, which corresponds to a “weighted” coin. But weighted coins don’t exist! If it were practical to manufacture trick coins with arbitrary biases, coin flipping wouldn’t be as popular as it is.
Yeah, and it’s so very easy to make a weighted die. Why don’t teachers switch to talking about weighted dice when explaining biased variables? You can label the sides of a six sided die with three 1s and three 2s to get a binary die easily enough. Just seems weird that something which is very physically difficult to ever make exist, and almost certainly nobody in the class has ever seen would be chosen as a teaching example over something which does exist and could even be made into a physical object for in-class demonstrations!
The coin flip is a brilliant piece of technology for generating trustworthy random noise:
Making a two-headed coin is forgery, which is a crime.
Such trick coins can be foiled anyways by calling the toss in the air.
Thus when teaching the concept of a Bernoulli variable, we use the example of coin flips, because everyone already knows what they are. This is unfortunate because the very next concept we introduce is a biased Bernoulli variable, which corresponds to a “weighted” coin. But weighted coins don’t exist! If it were practical to manufacture trick coins with arbitrary biases, coin flipping wouldn’t be as popular as it is.
Yeah, coins can only be weighted very slightly. See Andrew Gelman & Deborah Nolan: You Can Load a Die, But You Can’t Bias a Coin
Yeah, and it’s so very easy to make a weighted die. Why don’t teachers switch to talking about weighted dice when explaining biased variables? You can label the sides of a six sided die with three 1s and three 2s to get a binary die easily enough. Just seems weird that something which is very physically difficult to ever make exist, and almost certainly nobody in the class has ever seen would be chosen as a teaching example over something which does exist and could even be made into a physical object for in-class demonstrations!