Timeline for If all the marginal distributions are continuous, then the joint distribution is continuous?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 6, 2020 at 16:56 | comment | added | Dilip Sarwate | There is a pdf on the straight line but it is not a joint pdf which has units probability mass per unit area but rather a univariate pdf measured in units of probability mass _per unit length as measured along the straight line. Looked at another way, the joint CDF $F_{X,Y}(x,y)=P(X\leq x,Y\leq y)$ is not continuous everywhere in the plane, and so is not differentiable everywhere in the plane either, and so we cannot write $f_{X,Y}(x,y)=\frac{\partial^2}{\partial x \partial y}F_{X,Y}(x,y)$ as we can for jointly continuous random variables. | |
| Oct 6, 2020 at 15:07 | vote | accept | Star | ||
| Oct 5, 2020 at 23:59 | comment | added | Star | Thanks. Your example seems close to the first example of the other answer. However, the other answers seems to say that there can be a proper pdf on the line $y=x$. Which one is correct? | |
| Oct 5, 2020 at 21:15 | vote | accept | Star | ||
| Oct 5, 2020 at 23:56 | |||||
| Oct 5, 2020 at 20:36 | history | answered | Dilip Sarwate | CC BY-SA 4.0 |