I'm struggling to prove analytically that for two iid (independent and identically distributed) random variables $ P(X<Y) = 0.5$ for any distribution. I'm able to do it by direct integration on specific distributions, but not in the general usecase.
2026-04-22 07:08:30.1776841710
Proof that the probability $P(X<Y) = 0.5$ for two iid variable
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