(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Homework Help: Derivation question

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