Timeline for Rigorous proof of the duality of Coupon collector's problem and Occupancy problem
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 15, 2012 at 9:06 | vote | accept | user20886 | ||
| Apr 9, 2012 at 11:13 | answer | added | Did | timeline score: 6 | |
| Apr 4, 2012 at 23:18 | comment | added | Andreas Blass | Why do you say the space of all sequences of picks is unmeasurable? It seems to carry a perfectly good product measure, with respect to which the event you're interested in (described by the equivalent inequalities $L\geq l$ and $T\leq m$ or by the plain statement that there are at least $l$ different coupons among the first $m$ terms of the sequence) is a measurable set. So I don't see any real problem here. | |
| Apr 3, 2012 at 19:38 | comment | added | user20886 | Okay then, what is the sample space that these events are defined over? T and L can be described as random variables over the set of all sequences of picks which is uncountable and un-measureable. Though i suppose i could truncate it to all sequences of length m and allow T to be "Never". But then we can't define its variance or expectation, and its those that i am interested in. | |
| Apr 3, 2012 at 16:42 | comment | added | Ed Dean | Unless I'm missing something, it follows immediately from the setup/definitions that $T\leq m$ if and only if $L\ge l$. Indeed, the text of your question seems to take it for granted that each of these just gives a different description for the event "we win." | |
| Apr 3, 2012 at 15:49 | history | asked | user20886 | CC BY-SA 3.0 |