On a property of probabilistic context-free grammars
It is proved that for a probabilistic context-free language L(G), the population density of a character (terminal symbol) is equal to its relative density in the words of a sample S from L(G) whenever the production probabilities of the grammar G are estimated by the relative frequencies of the corresponding productions in the sample.
Link to Published Version
Chaudhuri, R., & Rao, A. N. V. (1983). On a property of probabilistic context-free grammars. International Journal of Mathematics and Mathematical Sciences, 6(2), 403–407. doi:10.1155/S0161171283000356