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Math Help - Chebyshev inequality

  1. #1
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    Chebyshev inequality

    Hi all,
    I would appreciate if someone could help me with this question.

    How I can ,using Chebyshev inequality, prove that a least  ${15}/{16}$ of all bitstrings $x \in \{0,1\}^n$ of length n have hamming weight that could satisfy the following relation  $ {n}/{2} - {4 \sqrt{n}}/{2} \leq wt(x) \leq {n}/{2} + {4 \sqrt{n}}/{2}$. wt(x) is hamming wieght.

    Thanks in advance

    Regards,
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  2. #2
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    Re: Chebyshev inequality

    I think you have to make the assumption that all the bitstrings are equally likely. With that assumption, the hamming weight has a Binomial(n, p) distribution with p = 1/2. From this you can get the mean and standard deviation and apply Chebyshev's inequality.
    Thanks from robmas
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