As anyone who has worked in probability knows, a random variable can sometimes behave in rather “unreasonable” ways. It may be never close to its expectation. It might exceed its expectation almost always, or almost never. It might have finite $1$st, $2$nd, and $3$rd moments, but an infinite $4$th moment. All of this poor behaviour [...]

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Gautam Kamath: Is $q'$ defined here?Gautam Kamath: On this page, Hölder is displaying for me as H{ö}lder - is t...Ryan O'Donnell: Yes, you're right. This is not a well-written proof by the ...Ryan O'Donnell: Thanks, yes.Ryan O'Donnell: Yep, thanks.Ryan O'Donnell: Yep, thanks.Noam Lifshitz: I think that in exercise 23, it should be $(p,2)$ Hypercontr...