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the characteristic function of a Gaussian random variable X distributed as $N(\mu,\sigma^2)$ is given by $\phi(w)=\exp(j\mu w-\frac{\mu^2 w^2}{2} )$

Please find the Chernoff Bound for the above Gaussian random variable.

Chernoff Bound is given by $P\{X>a\} \le \frac{\mathbb E[\exp(sX)]}{\exp(sa)}$ for $s>0$

I have no idea to think the solution of this question, can anyone help me?

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    The characteristic function is $\phi(w) = E(e^{iwX}).$ In the same way that it is calculated, you can calculate $E(e^{sX})$ – 2017-02-03
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    @spaceisdarkgreen, in fact, the mgf is calculated much easier (here finding chf by definition requires integration in the complex domain with some technicalities). – 2017-02-03

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