Quote:
Originally Posted by gordonbr
I'm confused about the process of determining whether a particular random sample "satisfies" Hoeffding's inequality.
In particular, when we run some experiments and determine the average proportion of green marbles, we generate some averages for several values. Can't we say that all of these values satisfy Hoeffding's Inequality, since Hoeffding's Inequality only says that the probability of something bad happening (i.e., not tracking ) for a random sample is small? I would think that any satisfies this condition, regardless of how we determined the sample.
I suppose my question is: how does a particular value fail to satisfy an inequality that seems to be a blanket statement for all possible values?

If the expression "satisfies Hoeffding's inequality" is used for a particular
, it is informal or figurative. It just says that this particular
is within
of
. Hoeffding asserts that this is likely to be the case, hence the word "satisfies."
The formal statement would not involve an individual
, but rather a full experiment, and it would be a statement that Hoeffding's inequalty holds under the conditions of such experiment. For instance, the multiplebin experiment does not satisfy the basic Hoeffding inequality.