Timeline for A probability question related to combinatoric problem
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| May 25, 2016 at 21:01 | comment | added | Elena Yudovina | Since FTXX is able to compute this quantity recursively, I'm guessing the question is asking for the probability of visiting the state $(m,n)$ as a function of $m$ and $n$ (as well as $q_A$, $q_B$, $q_C$); presumably $N = m+n$ and the queues are initially empty. It seems easier to think about the difference $m-n$ which is doing a version of a simple random walk, but I don't know of a nice exact expression for the distribution of a random walk whose transition probabilities depend on sign. There should be nice exact expressions for asymptotics such as $lim_{N \to \infty} P(m < n)$. | |
| May 25, 2016 at 10:07 | comment | added | Ben Barber | What probability do you want to compute? The probability that $Y$'s queue is ever longer than $X$'s, the probability that $Y$'s queue is longer than $X$'s at some given time, or something else? And can you say something about why you are interested in this problem? | |
| May 24, 2016 at 3:07 | history | asked | KevinKim | CC BY-SA 3.0 |