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
7 events
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| Apr 17, 2019 at 6:17 | history | edited | Xi'an | CC BY-SA 4.0 |
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| Apr 16, 2019 at 4:28 | comment | added | Xi'an | @whuber: right and right. I assumed continuity in addition to independence. | |
| Apr 16, 2019 at 4:26 | history | edited | Xi'an | CC BY-SA 4.0 |
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| Apr 16, 2019 at 0:50 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Apr 15, 2019 at 21:12 | comment | added | StatCurious | Sorry for any confusion. I cannot assume independence. I've updated the question to make it clear. | |
| Apr 15, 2019 at 20:42 | comment | added | whuber♦ | You could have stopped at the first line by noting that $F_Y(y) \ge 0$ for all $y\in \mathbb R$ implies $\mathbb{E}^Y[F_Y(Y)] \gt 0.$ I don't fully believe the rest of the calculation because I can find discrete variables $Y$ where this expectation does not equal $1/2.$ A uniform distribution on $\{0,1,2\}$ will work as a counterexample. | |
| Apr 15, 2019 at 20:29 | history | answered | Xi'an | CC BY-SA 4.0 |