Open Problem Garden - Sums of independent random variables with unbounded variance - Comments

Open Problem Garden - Sums of independent random variables with unbounded variance - Comments http://openproblemgarden.org/op/sums_of_independent_random_variables_with_unbounded_variance Comments for "Sums of independent random variables with unbounded variance" en Sums of independent random variables with unbounded variance http://openproblemgarden.org/op/sums_of_independent_random_variables_with_unbounded_variance <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/feige_uriel">Feige</a>   </td> <td align=right> Subject: <a href="/category/theoretical_computer_science">Theoretical Comp. Sci.</a>   </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>   If <img class="teximage" src="/files/tex/cc1036d1e1d6b5c9517091717d37abff019a4c74.png" alt="$ X_1, \dotsc, X_n \geq 0 $" /> are independent random variables with <img class="teximage" src="/files/tex/e0268221532981debea25e9446c8ee6f112e1881.png" alt="$ \mathbb{E}[X_i] \leq \mu $" />, then <img class="teximage" src="/files/tex/03dc1130142ee6fefcc33888e2fb6137211bf327.png" alt="$$\mathrm{Pr} \left( \sum X_i - \mathbb{E} \left[ \sum X_i \right ] < \delta \mu \right) \geq \min \left ( (1 + \delta)^{-1} \delta, e^{-1} \right).$$" /> </div> </tr></td> </table> </td> </tr> </table> Feige, Uriel Inequality Probability Theory randomness in TCS Theoretical Computer Science http://openproblemgarden.org/op/sums_of_independent_random_variables_with_unbounded_variance#comment Thu, 02 Apr 2009 04:08:59 +0200 cwenner 36887 at http://openproblemgarden.org