Timeline for If all the marginal distributions are continuous, then the joint distribution is continuous?
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6 events
| when toggle format | what | by | license | comment | |
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| Oct 6, 2020 at 17:23 | comment | added | kjetil b halvorsen♦ | See stats.stackexchange.com/questions/298293/… for details about absolute continuity! | |
| Oct 6, 2020 at 0:01 | comment | added | kjetil b halvorsen♦ | In both examples the vector $X$ is concentrated on a set with measure 0 with respect to Leb measure on the plane. So it is not absolutely continuous with respect to that measure. This makes clear that in these examples we need to be more precise with the terminology! | |
| Oct 5, 2020 at 23:58 | comment | added | kjetil b halvorsen♦ | A density is always with respect to a base measure There can be no density on $y=x$ with respect to Leb Measure on the plane (as then the line has measure 0), but it can be *with respect to Leb measure on the line itself. | |
| Oct 5, 2020 at 23:55 | comment | added | Star | Also the first example seems to contradict with the other answer which says that there can't be a proper pdf on the line $y=x$ | |
| Oct 5, 2020 at 23:54 | comment | added | Star | Thanks, but in both examples the vector $X$ is continuosly distributed (although not with support equal to the plane). Hence it does not contradict my statement. | |
| Oct 5, 2020 at 21:28 | history | answered | kjetil b halvorsen♦ | CC BY-SA 4.0 |