Timeline for If $F_X(z) > F_Y (z)$ for all $z\in \mathbb{R}$ then $P(X < Y ) > 0$?
Current License: CC BY-SA 4.0
10 events
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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
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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.
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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 |