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Math Help - Binomial distribution

  1. #1
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    Binomial distribution

    Let X be Binomial B(p,n) with p>0 fixed, and a>0. How can I show that:

    P(|\frac{X}{n}-p|>a)\le\frac{\sqrt{p(1-p)}}{a^2n}min(\sqrt{p(1-p)},a\sqrt{n})
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  2. #2
    MHF Contributor matheagle's Avatar
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    To be smaller than the min, means it's smaller than both.
    Clearly the first is true by chebyshev's
    That means you must also prove that

    P\left( \left| {X\over n}-p\right|>a\right)\le {\sqrt{p(1-p)}\over a\sqrt{n}}

    and that's just the st deviation over a, which is markov.
    Last edited by matheagle; September 22nd 2010 at 01:38 PM.
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