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Derivation question

  1. Dec 28, 2008 #1
    1. The problem statement, all variables and given/known data

    To derive the Bernsteine inequality

    [tex]P[\left|f(x)\right| \ge z] \le 2e^{-z^2/2}[/tex]

    Start with,

    [tex]P[f(x) \ge z] \le e^{-cz+{\frac{c^2}{2}}[/tex]

    2. Relevant equations

    [tex]P[\left|f(x)\right| \ge z] \le \frac{1}{z^2}[/tex]

    3. The attempt at a solution

    The first thing to do is to set the function in the Probability constraint to the absolute value

    [tex]P[\left|f(x)\right| \ge z] \le 2.e^{-cz+{\frac{c^2}{2}}[/tex]

    [tex]P[\left|f(x)\right| \ge z] \le 2.e^{-cz}.e^{\frac{c^2}{2}}[/tex]

    At the point I get confused. If [tex]e^{-cz}[/tex] is 1=> c or z must be zero. Any idea how to proceed?
     
  2. jcsd
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