Does the empty word count as a 'word'? If I have DFA accepting

$\{w \in \{a,b\}^*$ s.t. on every odd position in $w$ there is a $b\}$

Would the empty word be accepted? Also, would the word $eb$ be accepted?
The empty word belongs to the language, since on all its odd positions -- all zero of them -- we find a $b$.

$eb$ does not belong to $\{a,b\}^*$, hence it does not belong to the language.