A Cauchy Distribution is a perfectly valid probability distribution, but has an undefined meanpic.twitter.com/eNMBzSeGa6
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Yes, it’s really undefined. The mean is defined by an integral whose value is undefined. We don’t get to pick how we take the limit: it has to converge no matter what we do. This isn’t a choice: if we do it like the above, the core theorems that underly stats break
