Timeline for Probabilities related to distributing $n$ items into $m$ containers
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 8 at 15:41 | vote | accept | Benjamin Kay | ||
| Jan 8 at 2:52 | comment | added | Ben | @Henry: The coupon-collector distribution is a slightly different distribution which forms the solution to an inverse problem relating to this situation (see e.g., O'Neill 2022). | |
| Jan 8 at 0:10 | history | edited | Ben | CC BY-SA 4.0 | added 6 characters in body; edited title |
| Jan 8 at 0:08 | answer | added | Ben | timeline score: 4 | |
| Jan 7 at 22:54 | comment | added | Henry | The probability of a particular child getting $k$ ice creams is simpler: that distribution has a binomial distribution with parameters $10$ and $\frac1{20}$. But what happens to a particular child is not independent of what happens to the others. | |
| Jan 7 at 22:49 | comment | added | Henry | I might call it the coupon-collector distribution. There are previous related questions here but briefly, the probability of $x$ children getting at least one ice cream is $S_2(10,x) \, 20! / ((20-x)!\, 20^{10})$ where $S_2(,)$ is a Stirling number of the second kind, the expected number is $20(1-(1-1/20)^{10})$ and the variance is $20(1-1/20)^{10} + 20^2(1-1/20)*(1-2/20)^{10} - 20^2 (1-1/20)^{2\times10}$ | |
| S Jan 7 at 21:57 | review | First questions | |||
| Jan 8 at 5:18 | |||||
| S Jan 7 at 21:57 | history | asked | Benjamin Kay | CC BY-SA 4.0 |