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Math Help - chebyshev inequality

  1. #1
    Member roshanhero's Avatar
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    chebyshev inequality

    In general what does the chebyshev inequality refers and how can I prove this theorem using integral signs?
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    MHF Contributor matheagle's Avatar
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    as usual I don't understand your questions
    what is 'integral signs'?
    The proof consists of splitting the integral into two pieces and throwing away one
    and using an inequality on the other
    http://en.wikipedia.org/wiki/Chebyshev's_inequality
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  3. #3
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    Quote Originally Posted by roshanhero View Post
    In general what does the chebyshev inequality refers and how can I prove this theorem using integral signs?
    http://people.csail.mit.edu/ronitt/COURSE/S07/lec25.pdf

    Chebyshev's inequality: Definition from Answers.com
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    Member roshanhero's Avatar
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    A symmetrical die is thrown 600 times.What is the lower bound of getting 80 to 120 sixes?
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  5. #5
    MHF Contributor matheagle's Avatar
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    that's a binomial problem that can be fairly approximated with the normal ditsribution via the central limit theorem

    n=100, p=1/6 hence the mean is 100
    you need to figure out what 20 is in terms of the st. deviation
    the variance is npq
    Last edited by matheagle; July 12th 2009 at 05:28 PM.
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  6. #6
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    Quote Originally Posted by matheagle View Post
    that's a binomial problem that can be fairly approximated with the normal ditsribution via the central limit theorem

    n=100, p=1/6 hence the mean is 100
    you need to igure out what 20 is in terms of the st. deviation
    the variance is npq
    But the "standard deviation" is defined as the square root of the variance. Since the variance is "npq", the standard deviation is \sqrt{npq}= \sqrt{100(1/6)(5/6)}= \frac{10}{6}\sqrt{5}= \frac{4\sqrt{5}}{3}

    20 is \frac{20}{\frac{4\sqrt{5}}{3}}= \frac{15}{\sqrt{5}}= 3\sqrt{5} standard deviations.
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  7. #7
    Member roshanhero's Avatar
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    That question needs to be done by using chebyshev inequality.
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  8. #8
    MHF Contributor matheagle's Avatar
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    we answered that
    20 is how many st deviations...
    HENCE, divide 20 by \sqrt{npq} and plug that into chebyshev's

    AND lower bound on what?
    we assume you mean probabilities here.
    solve for k and plug into the inequality on either of those links.
    Last edited by matheagle; July 12th 2009 at 10:15 PM.
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