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Old 10-18-2012, 05:46 PM
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yaser yaser is offline
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Location: Pasadena, California, USA
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Default Re: Q2.2/Hoeffding clarifications

Originally Posted by chris View Post
Regarding my second question, I was trying to determine whether Hoeffding can be applied to v_min using mu = the expected minimum fraction of heads from 10 flips of 1000 coins (<< 0.5 for unbiased coins) rather than mu = the expected fraction of heads from 10 flips of a single coin (0.5 for an unbiased coin).
Hoeffding cannot be directly applied, but more general forms that use expected values and variances of general random variables (rather than just the probability of an event and the frequency of occurence of that event) can be applied.

Specifically, I would like to understand the difference between 2 approaches to estimating the probability of flipping a head from a Hoeffding perspective (1) averaging the fraction of heads realised by 10 coin flips over 100,000 experiments, and (2) the fraction of heads realised by 1,000,000 repetitions of a single flip.
Hoeffding can be directly applied to (1), the event being "ten heads out of 10 flips," whereas (2) involves the expected value of a random variable as discussed above.
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