Timeline for Number of duplicate pairs in multiple samplings
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 17, 2020 at 22:44 | vote | accept | OmarR | ||
| Aug 17, 2020 at 20:05 | answer | added | Iosif Pinelis | timeline score: 2 | |
| Aug 17, 2020 at 20:00 | comment | added | OmarR | @losifPinelis. Exactly! Thanks for clarifying. | |
| Aug 17, 2020 at 19:51 | comment | added | Iosif Pinelis | @OmarR. : Does "any pair of items (i,j) that is found more than once across samplings" mean "any subset of cardinality $2$ of the set $\{1,\dots,M\}$ that is found in more than one sampling"? | |
| Aug 17, 2020 at 19:49 | comment | added | OmarR | Could you please explain how the probability $9(n^2-n)/(M^2-M)$ is obtained because this formula does not make a distinction between sampling with and without replacement (I guess). | |
| Aug 17, 2020 at 18:10 | comment | added | user44143 | Each of the 10 times, $(n^2-n)/2$ pairs are chosen. For each pair at one time, the probability of its matching with a pair from another time is roughly $9(n^2-n)/(M^2-M)$. So the expected number of duplicate pairs is roughly $$\frac{45(n^2-n)^2}{2(M^2-M)}.$$ Since $n << M$, it seems unnecessary to go further. | |
| Aug 17, 2020 at 16:58 | comment | added | OmarR | Any pair of items (i,j) that is found more than once across samplings. | |
| Aug 17, 2020 at 15:58 | comment | added | Iosif Pinelis | What do you mean by a pair duplicate? | |
| Aug 17, 2020 at 15:34 | history | asked | OmarR | CC BY-SA 4.0 |