You are correct. We could have made other assumptions.
But there is a special reason why we DO want 1. Because we are bounding the probability, and so there is nothing to prove if we claim that a probability is less equal to 1. So, whenever the RHS (i.e. the bound) evaluates to 1 or bigger, there is nothing to prove. So we only need to consider the case when the bound evaluates to less than 1.
Quote:
Originally Posted by CountVonCount
Hello,
thanks for the answer. I understand this argument, however this holds also for
or for
Thus the value 1/4 is somehow magic for me.
Edit: I think you choose 1/4 because it is so easy to see, that the RHS of Theorem A.1 gets 1. Nevertheless with a different value you would get a different outcome of the final formula.
