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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.

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?

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 incomprehensible – Anthony Quas Apr 29 2011 at 7:35
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 your use of the word "scale" is either non-standard, or else not explained very clearly. Could you please explain what you mean by "we scaled the left side to the right side" and "the scale level is too large"? – Yemon Choi Apr 29 2011 at 9:07
Your question does not seem to be well-formed (for example, you never used $\eta$), and the part I understand does not seem to be at an appropriate level for MathOverflow. Please see the FAQ for a list of websites that might be better matches for your question. – S. Carnahan♦ May 1 2011 at 4:59

closed as not a real question by Franz Lemmermeyer, Andres Caicedo, S. Carnahan♦ May 1 2011 at 4:59

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