Thread: role of P(X) ?
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Old 09-17-2015, 09:28 PM
ilson ilson is offline
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Default 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 p=\mu.

This condition can actually be relaxed to any N non-identical 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 Azuma-Hoeffding inequality).
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