We assume without loss of generality that the two Poisson parameters for
a given term, 
and 
, are appropriate for documents of
average length. Then the Verbosity hypothesis would imply that while a
longer (say) document has more words, each individual word has
the same probability of being the term in question. Thus the
distribution of term frequencies in documents of length d will be
2--Poisson with means 
and 
.
We may also make various independence assumptions, such as between document length and relevance.