More precisely, for each X ∈ N ∪ W a PCFG associates distributions G X over the set of trees T X generated by X as follows: If X ∈ W (i.e., if X is a terminal) then G X is the distribution that puts probability 1 on the single-node tree labelled X.
if X ∈ N (i.e., if X is a nonterminal) then: where R X is the subset of rules in R expanding nonterminal X ∈ N , and: TD X (G 1 , .