I Chernoff Bounds for Independent Bernoulli Sums

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WMDhamnekar
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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.
 
There is a nice little variation of the problem. The host says, after you have chosen the door, that you can change your guess, but to sweeten the deal, he says you can choose the two other doors, if you wish. This proposition is a no brainer, however before you are quick enough to accept it, the host opens one of the two doors and it is empty. In this version you really want to change your pick, but at the same time ask yourself is the host impartial and does that change anything. The host...

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