#1




Chapter 1  Exercise 1.9
Based on the marbles example, I understand that u is the probability of choosing a red marble from the bin of marbles and v is the fraction of red marbles in the sample of chosen marbles. And I think that the LHS of the Hoeffding Inequality represents the probability of v deviating from u being greater than the error bar epsilon. Now, I am not sure how I should choose an epsilon to evaluate this probability and where I should begin. Can someone point me in the right direction?

#2




Re: Chapter 1  Exercise 1.9
If and , it implies that (any number slightly less than 0.8). By the implication bound,
By looking at the RHS, one can identify for applying the Hoeffding bound.
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#3




Re: Chapter 1  Exercise 1.9
Since we're only looking at epsilon applied in one direction, meaning that we're only interested in nu being mu  0.8 and not mu + 0.8, should we drop the leading 2 from the bound calculation? I'm not sure if I'm interpreting this bound correctly or simply overthinking things.

#4




Re: Chapter 1  Exercise 1.9
You are right. If al you want is the "one sided deviation", you could drop the factor of 2. However keeping the factor of 2 is a worse but still valid bound.
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#5




Re: Chapter 1  Exercise 1.9

#6




Re: Chapter 1  Exercise 1.9

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