#11




Re: role of P(X) ?
To add to professor's explanation, another way to put it is that the Hoeffding inequality as presented in the book applies to sequence of N i.i.d. Bernoullli random variables with parameter .
This condition can actually be relaxed to any N nonidentical but independent r.v.'s that almost surely take values on compact intervals. There's even a further generalization that does not even require independence, so long as the sequence is a Martingale with (a.s.) bounded increments (see AzumaHoeffding inequality). 
#12




Re: role of P(X) ?
I had the same question, I still don't know if we need to know P(X) or not! I know it doesn't matter which P(x) is used but should we know it or not?
it seems we just should select examples randomly and independently (what it actually means?) How we can get sure we do as this? 
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