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Old 04-14-2012, 12:00 AM
jsarrett jsarrett is offline
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Join Date: Apr 2012
Location: Sunland, CA
Posts: 13
Default Re: question about probability

Hoeffding's inequality has a free parameter in your question, namely \epsilon. It lest you say that since you have 10 samples, if you want to be 80% sure of the distribution of marbles in the jar (\epsilon = 0.2), then the jar is at most E_{out} percent different from the sample.

where
P(|E_{in}-E_{out}|
 < \epsilon) \le 2e^{-2\epsilon^2N}

substituting from your example:
P(|0-E_{out}| < 0.2) \le 2e^{-2(0.2^2)10}

simplifying:
P(|0-E_{out}| < 0.2) \le 0.898657928234443
so we think that with 80% confidence, the jar is at least 10.2% green.

We probably need a bigger N!
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