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Old 04-21-2012, 11:32 PM
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yaser yaser is offline
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Location: Pasadena, California, USA
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Default Re: Exercise 1.10

Originally Posted by pablo View Post
Since this is a theory week, thought this might be a good time to explore Hoeffding a bit.

I understand c_1 and c_rand satisfy Hoeffding experimentally as described, but conceptually does c_rand satisfy Hoeffding? For example, suppose it is unknown whether each coin is fair (or that they are known to have varying fairness - e.g. c_1 is 50/50, c_2 is 40/60, etc.). Would each coin represent a separate 'bin' or would the random selection of a coin plus the ten flips represent the randomized selection condition for c_rand?

Trying to understand if it's necessary for the coins to be identical.
Interesting question indeed. Hoeffding does apply to each randomly selected coin individually as you point out. If the coins have different values of E_{\rm out}, then the added randomization due to the selection of a coin affects the relationship between E_{\rm in} and E_{\rm out}. This is exactly the premise of the complete bin model analysis.
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