Consider the following probabilistic context free grammar. sNP VP NP Adj NP NP PRP NP N VP V NP VP Aux V NP PRP they N potatoes Adj baking V baking [1,0] [0.3] [0.6] [0.8] [0.2] [1.01 1.0] 1.o] [0.5] [0.5] 1.0 are Aux are (a) Using this grammar, show how the Earley algorithm would parse the following sentence. they are baking potatoes Write down the complete parse chart. The chart should contain n+1 entries where n is the length of the sentence. Each entry i should contain all parser items generated by the parser that end in position i You can ignore the probabilities for part (a) (b) Write down all parse trees for the sentence and grammar from problem 2 and compute their probabilities according to the PCFG Consider the following probabilistic context free grammar. sNP VP NP Adj NP NP PRP NP N VP V NP VP Aux V NP PRP they N potatoes Adj baking V baking [1,0] [0.3] [0.6] [0.8] [0.2] [1.01 1.0] 1.o] [0.5] [0.5] 1.0 are Aux are (a) Using this grammar, show how the Earley algorithm would parse the following sentence. they are baking potatoes Write down the complete parse chart. The chart should contain n+1 entries where n is the length of the sentence. Each entry i should contain all parser items generated by the parser that end in position i You can ignore the probabilities for part (a) (b) Write down all parse trees for the sentence and grammar from problem 2 and compute their probabilities according to the PCFG