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Apr 16, 2019 at 12:01 history tweeted twitter.com/StackStats/status/1118122136441425920
Apr 16, 2019 at 0:54 vote accept StatCurious
Apr 16, 2019 at 0:23 answer added Ben timeline score: 7
Apr 15, 2019 at 23:48 history edited Ben CC BY-SA 4.0
deleted 7 characters in body
Apr 15, 2019 at 21:53 comment added whuber I found counterexamples by considering discrete variables supported on $\{0,1,2\}$ and constructing a table with given marginals (nearly satisfying your requirements, for of course the two distribution functions must agree on $(-\infty,0)$ and $(,\infty)$) and distributing the probability within the tables to make $\Pr(X\lt Y)$ very small. This provides the insight; such near-counterexamples are readily modified into genuine counterexamples.
Apr 15, 2019 at 21:09 history edited StatCurious CC BY-SA 4.0
updated question to make it clear that you are to prove or disprove and added that independence may not be assumed.
Apr 15, 2019 at 21:08 comment added StatCurious @whuber, sorry, I wasn't clear about this earlier. The question asks to prove OR disprove that this is true. We may NOT assume independence.
Apr 15, 2019 at 20:29 answer added Xi'an timeline score: 3
Apr 15, 2019 at 20:12 comment added whuber This isn't true. Does the question ask you to assume $X$ and $Y$ are independent?
Apr 15, 2019 at 19:32 history asked StatCurious CC BY-SA 4.0