Chernoff Bounds for Independent Bernoulli Sums

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WMDhamnekar
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TL;DR
What is wrong with this proof? Can you notice that? or I am wrong. In my opinion, in the R.H.S. of inequality (3.2), the index of 'e' must be positive if we use the proof. I also want to know how to derive the proof of inequality(3.3)? Author said it is similar to that of (3.2). But I don't understand that.
Chernoffbounds proof.png
 
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I cleared my doubt taking suitable guidelines from other statistician on Internet.
 

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