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.