User knighter - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T11:16:05Z http://mathoverflow.net/feeds/user/1155 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/63384/a-problem-with-inequality-scale A problem with inequality scale knighter 2011-04-29T07:21:19Z 2011-04-29T07:36:14Z <p>According to the below inequality : $$E\big[\sqrt{\sum_{m=1}^{M}z_{m}^{i}}\big]\geq{E\big[\sqrt{M}\sqrt[2M]{\prod_{m=1}^{M}z_m^i\big]}}={E\big[\sqrt{M}\prod_{m=1}^{M}z_m^i\big]}$$ we scaled the left side to the right side, where $\eta$ is constant vector, and $z_m$ is random, binary, unit-basis vector.</p> <p>But we found the scale level is too large. We wanna remove the sqrt of the left side and have a moderate scale, are there any approach?</p>