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Will_Sawin comments on When is further research needed? - Less Wrong
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Or in other words, the expectation of a max of some random variables is always greater or equal to the max of the expectations.
You could call this 'standard knowledge' but it's not the kind of thing one bothers to commit to memory. Rather, one immediately perceives it as true.
"one" is not general enough. Do you really think what you just said is true for all people?
It's true for anyone who understands random variables and expectations. There's a one line proof, after all.