Timeline for Order statistics of iid uniform RV and Pólya's urn model. Question about a.s. convergence
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| Sep 2, 2016 at 16:49 | comment | added | fedja | @user240643 If you have plenty of independent random events of a fixed probability (however small), then the probability that at least one happens is close to $1$. So, just choose $\ell$ so small that for the vast majority of $\omega\in\Omega$ you can find $1/\mu_n$ or so $\ell$-separated values among $U_k(\omega)$ with $k\ge n$. | |
| Sep 2, 2016 at 15:31 | comment | added | user240643 | Thank's a lot for your answers! I understand the other answer, but I have some troubles with this one...First of all: Yes, no fixed vairable is equal to the limiting one a.s. I have some trouble handling the 'random-set-construction' of the counter example...Why is $P(\text{there is $k>n$ such that $U_k\in A_n$})>1/2$? | |
| Sep 2, 2016 at 3:42 | history | answered | fedja | CC BY-SA 3.0 |