I think you have to be a physicist (not mathematician) to find this notable.
A Cauchy Distribution is a perfectly valid probability distribution, but has an undefined meanpic.twitter.com/eNMBzSeGa6
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weird flex
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I don't think "→∞" is the right way to say what goes wrong with this integral. You can find open sets U_i whose union is the real line such that the integral of this function over U_i approaches *whatever you want* - any finite number, or +∞, or -∞ - or doesn't converge.
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that's a good point.. i was worrying about that after i saw
@AndrewM_Webb 's animation - 1 more reply
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Related to not having a defined mean: no matter how many samples you already have from a Cauchy, the next sample can shift the sample mean arbitrarilypic.twitter.com/4nSrigOwri
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In fact, the sample mean is no more informative about the distribution's location parameter than any single sample is!
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Hey Dillon, would you like to sit my clasical mechanics exam for me today?
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lol na you got this! but i do love me some classical mechanics
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Wait... What?? How can that happen? Definitely have to look it up on google or somewhere
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a bunch of really nice stuff here in the comments
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