Probabilistic Context Grammars

Problem One		For this exercise you will use this partial PCFG: S → NP VP .80 Det → the .40 NP → Det N .30 Det → a .40 VP → V NP .20 N → meal .01 V → includes .05 N → flight .02 Fill out the rest of this chart
Problem Two		Modify your version of a CKY recognizer to compute the probability of the most probable parse, using the probabilistic CKY algorithm of Chapter 14 (Ney 1991). Here is the pseudocode: You do not have to return a parse tree as the pseudocode does. You need only the return the probability of the most probable parse. (This is the probabilistic version of a recognizer). You may also want to review the class notes here. You will want to use the Python implementation of a CKY parser gievn in the online Parser writing help notes.. Check your answer on the PCFG above using the probability calculations you did in Problem One.