most recent 30 from http://mathoverflow.net 2013-05-21T12:14:51Z http://mathoverflow.net/feeds/user/7238 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/93787/affect-of-noise-on-random-variable-separation Kishor Barman 2012-04-11T17:25:17Z 2012-04-11T17:45:30Z

<p>We have two random variables $X$ and $Y$. Suppose $P_1$ is the probability that $Pr[X > Y]$. $Z_1$ and $Z_2$ are two i.i.d. (identical and independent) random variables, and let $P_2$ be the probability that $Pr[X+Z_1 > Y+Z_2]$. </p> <p>Can $P_2$ be greater than $P_1$?</p> <p>If we think $Z_1$ and $Z_2$ as noise, then in words, can adding i.i.d noise make two random variables more separable?</p>

http://mathoverflow.net/questions/30742/limit-probability Kishor Barman 2010-07-06T08:49:52Z 2010-07-06T13:27:48Z

<p>You start with a bag of N recognizable balls. You pick them one by one and replace them until they have all been picked up at least once. So when you stop the ball you pick has not been picked before but all the others have been picked once or more.</p> <p>Let $P_N$ be the probability that all the others were actually picked twice or more.</p> <p>Questions: does $P_N$ have a limit as $N\to \infty$, is this limit 0 or can you compute it?</p> <p>Note: This is a question that was asked at the Yahoo answers forum, by gianlino. Since no one has found an answer in that forum, I forwarded it here. Here is the original link. <a href="http://answers.yahoo.com/question/index;_ylt=ApZ_Q6sS137DnEcNoUBqn.vty6IX;_ylv=3?qid=20100704050924AAfLYYJ" rel="nofollow">http://answers.yahoo.com/question/index;_ylt=ApZ_Q6sS137DnEcNoUBqn.vty6IX;_ylv=3?qid=20100704050924AAfLYYJ</a></p>