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Math Help - chebyshev's inequality problem

  1. #1
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    Post chebyshev's inequality problem

    How can I use Chebyshev's Inequality to show that P[0 < X < 3] >= 0.75?
    note: X ~ Exp (lamba = 1)

    and does the Cheby. inequality improve as k --> infinity?

    it's a little confusing. can someone help?
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  2. #2
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    Quote Originally Posted by silentrain View Post
    How can I use Chebyshev's Inequality to show that P[0 < X < 3] >= 0.75?
    note: X ~ Exp (lamba = 1)

    and does the Cheby. inequality improve as k --> infinity?

    it's a little confusing. can someone help?
    There are things you need to make it your business to know:

    1. The statement of Chebyshev's Inequality.

    2. The mean of an exponential distribution.

    3. The standard deviation of an exponential distribution.


    Once you know these things you need to see that:


    \Pr(0 < X < 3) = \Pr(0 < X < \mu + 2 \sigma)

     = \Pr(\mu - 2 \sigma < X < \mu + 2 \sigma)

    since \mu - 2 \sigma < 0 and \Pr(X < 0) = 0

    = \Pr( - 2 \sigma < X - \mu < 2 \sigma) = \Pr(|X - \mu| < 2 \sigma)


    where \mu and \sigma are respectively the mean and standard deviation of X.
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