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magdon · #2 09-11-2013, 12:31 PM

If $\mu=0.9$ and $\nu\le0.1$ , it implies that $|\nu-\mu|>0.8^-$ (any number slightly less than 0.8). By the implication bound,

$P[\nu\le0.1] \le P[|\nu-\mu|>0.8^-]$

By looking at the RHS, one can identify $\epsilon$ for applying the Hoeffding bound.