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A certain little-known human language consists of only nouns and verbs. A sentence begins with a noun with probability 75% and with a verb with probability 25%. If a given word in a sentence is a noun, there is a 75% probability that the next word is a verb and a 25% probability that the next word is a noun. If a given word is a verb, there is a 75% probability that the next word in the sentence is a noun, and a 25% probability that is a verb. We can model this language using a Markov chain with two states: noun and verb.

A certain little-known human language consists of only nouns and verbs. A sentence begins with a noun with probability 75% and with a verb with probability 25%. If a given word in a sentence is a noun, there is a 75% probability that the next word is a verb and a 25% probability that the next word is a noun. If a given word is a verb, there is a 75% probability that the next word in the sentence is a noun, and a 25% probability that is a verb. We can model this language using a Markov chain with two states: noun and verb.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 3E
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A certain little-known human language consists of only nouns and verbs. A sentence begins with a noun with probability 75% and with a verb with probability 25%. If a given word in a sentence is a noun, there is a 75% probability that the next word is a verb and a 25% probability that the next word is a noun. If a given word is a verb, there is a 75% probability that the next word in the sentence is a noun, and a 25% probability that is a verb.

We can model this language using a Markov chain with two states: noun and verb.

 

A certain little-known human language consists of only nouns and verbs. A sentence begins with a noun with probability 75% and with a verb with probability 25%. If a given word in a sentence is a noun, there is a 75% probability that the next word is a verb and a 25% probability that the next word is a noun. If a given word is a verb, there is a 75% probability that the next word in the sentence is a noun, and a 25% probability that is a verb. We can model this language using a Markov chain with two states: noun and verb. To get some practice, draw the Markov chain that models this language on a piece of paper. The Markov chain has... (mark all that apply) O exactly 2 nodes and 4 directed edges exactly 2 nodes and 4 undirected edges O exactly 2 nodes and 2 directed edges O an edge from "noun" to "verb" that has a weight of 0.75 O an edge from "verb" to "noun" that has a weight of 0.25 2 What is the probability that the first three words of a sentence are all nouns? O around 1.56% O around 4.69% O around 14.06% O around 42.19% What is the probability that the third word of a sentence is a noun? O 21.875% © 25% O 56.25% O 37.5% 4 Finally, consider observing the sentence "Yacc grep." What is the most likely part-of-speech state sequence (i.e. sequence of nouns and verbs) that could have resulted in this sentence? As an exercise for now, just use a brute-force search over all 4 possible sequences, i.e. compute all 4 and choose the one with the highest probability. In the next lecture, we will see how to do this more efficiently using the Viterbi algorithm. O Noun Noun O Noun Verb O Verb Noun O Verb Verb
Transcribed Image Text:A certain little-known human language consists of only nouns and verbs. A sentence begins with a noun with probability 75% and with a verb with probability 25%. If a given word in a sentence is a noun, there is a 75% probability that the next word is a verb and a 25% probability that the next word is a noun. If a given word is a verb, there is a 75% probability that the next word in the sentence is a noun, and a 25% probability that is a verb. We can model this language using a Markov chain with two states: noun and verb. To get some practice, draw the Markov chain that models this language on a piece of paper. The Markov chain has... (mark all that apply) O exactly 2 nodes and 4 directed edges exactly 2 nodes and 4 undirected edges O exactly 2 nodes and 2 directed edges O an edge from "noun" to "verb" that has a weight of 0.75 O an edge from "verb" to "noun" that has a weight of 0.25 2 What is the probability that the first three words of a sentence are all nouns? O around 1.56% O around 4.69% O around 14.06% O around 42.19% What is the probability that the third word of a sentence is a noun? O 21.875% © 25% O 56.25% O 37.5% 4 Finally, consider observing the sentence "Yacc grep." What is the most likely part-of-speech state sequence (i.e. sequence of nouns and verbs) that could have resulted in this sentence? As an exercise for now, just use a brute-force search over all 4 possible sequences, i.e. compute all 4 and choose the one with the highest probability. In the next lecture, we will see how to do this more efficiently using the Viterbi algorithm. O Noun Noun O Noun Verb O Verb Noun O Verb Verb
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