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Old 04-16-2012, 07:20 AM
gordonbr gordonbr is offline
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Default What does it mean to "satisfy" Hoeffding's Inequality?

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 E_{in} values. Can't we say that all of these E_{in} values satisfy Hoeffding's Inequality, since Hoeffding's Inequality only says that the probability of something bad happening (i.e., E_{in} not tracking E_{out}) for a random sample is small? I would think that any E_{in} satisfies this condition, regardless of how we determined the sample.

I suppose my question is: how does a particular E_{in} value fail to satisfy an inequality that seems to be a blanket statement for all possible E_{in} values?
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