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If I have $x_1, x_2,\ldots, x_n$ independent NON-identically distributed Bernoulli random variables, how do I show that: $$\mathrm{Pr}\left(\sum_{i=1}^nx_i>\beta\mu\right)\le e^{-g(\beta)\mu}$$

where $$\beta>1$$$$\mu=E\left(\sum_{i=1}^nx_i\right)$$$$g(\beta)=\beta\times \ln(\beta)-\beta+1$$? I believe this can be accomplished using the Markov inequality (because that's what we've been covering), but I'm still not sure how to apply it.

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