Exercise 23.13

Consider the following PCFG:

$S \rightarrow NP \space VP[1.0] $

$NP \rightarrow \textit{Noun}[0.6] \space

\space \textit{Pronoun}[0.4] $

$VP \rightarrow \textit{Verb} \space NP[0.8] \space

\space \textit{Modal}\space \textit{Verb}[0.2]$

$\textit{Noun} \rightarrow \textbf{can}[0.1] \space

\space \textbf{fish}[0.3] \space

\space …$

$\textit{Pronoun} \rightarrow \textbf{I}[0.4] \space

\space …$

$\textit{Verb} \rightarrow \textbf{can}[0.01] \space

\space \textbf{fish}[0.1] \space

\space …$

$\textit{Modal} \rightarrow \textbf{can}[0.3] \space

\space …$

The sentence “I can fish” has two parse trees with this grammar. Show the two trees, their prior probabilities, and their conditional probabilities, given the sentence.