Chernoff Bounds for Independent Bernoulli Sums

[WMDhamnekar]

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.

 

[WMDhamnekar]

I cleared my doubt taking suitable guidelines from other statistician on Internet.