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Markov and Chebyshev Inequalities

  1. Aug 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Let X be a random variable; show that for a>1 and t>0,
    P(X>=(1/t)(ln(a)))<=(1/a)(Mx(t))


    2. Relevant equations



    3. The attempt at a solution

    I know, from a previous problem, that, where X is a random variable and K is a constant,
    P(X>t)<=E(exp(kX))/(exp(kt))

    For the right side of the equation of the problem, I know that Mx(t)=E(exp(tx)), which is the numerator of the equation, but I don't know how to show that the denominator ="a".

    Any helpful hints would be very much appreciated.
     
  2. jcsd
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