Hoeffding's inequality with M
Hi,
I'm wondering why in Lecture 2  when we're trying to modify the right hand side of Hoeffding's inequality to take into account drawing from multiple bins (see page 16 of the slides)  we sum all the probabilities of samples being nonrepresentative, rather than taking 1  the product of all the probabilities of each sample being representative.
In other words, (calling the right hand side of the original inequality p for simplicity) why doesn't the right hand side of the modified form become 1(1p)^M instead of M*p.
Wouldn't that be a still correct but tighter bound?
Thanks!
