Timeline for The difference of $\sum_{i=1}^{n}X_{i}$ and $\sum_{i=1}^{n}X_{(i)}$
Current License: CC BY-SA 4.0
4 events
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| Aug 25, 2023 at 6:51 | comment | added | Inforz | I think I know what confused me. For $X_{i}$ and $X_{(i)}$, they have different distribution. But for $\sum X_{i}$ and $\sum X_{(i)}$, they have the same distribution. And $X_{i}$ are i.i.d. but $X_{(i)}$ are not independent. | |
| Aug 25, 2023 at 4:05 | comment | added | kjetil b halvorsen♦ | But whatever is the data, the same argument can be made. There is no possibility of an outcome where the result does not hold. | |
| Aug 25, 2023 at 4:04 | comment | added | Inforz | When we observe the data, we can know the $\sum X_{i}$ is equal to the $\sum X_{(i)}$. But $X_{i}$ and $X_{(i)}$ are random variables, I am still a little confused. | |
| Aug 25, 2023 at 3:49 | history | answered | kjetil b halvorsen♦ | CC BY-SA 4.0 |