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.

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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.

 

**Understanding a Simple Markov Model in Linguistics**

A special human language is composed exclusively of nouns and verbs. A sentence begins with a noun with a 75% probability and with a verb at 25%. If a given word is a noun, there is a 75% likelihood the next word will be a verb, and a 25% chance it will be a noun. If a given word is a verb, there's a 75% chance the next word will be a noun and a 25% chance it will be a verb. This language can be modeled using a Markov chain with two states: noun and verb.

**1. Markov Chain Practice:**

When drawing the Markov chain for this language, it should feature:
- Only two nodes and four directed edges.
- Each nodal transition, such as from "noun" to "verb", will have a weight of 0.75, while "verb" to "noun" also carries a weight of 0.75.

**2. Probability of Initial Sentence Structure:**

Calculate the probability that the first three words of a sentence are all nouns:
- Approximately 4.69%.

**3. Determining the Third Word's Part of Speech:**

Identify the probability that the third word in a sentence is a noun:
- 25% chance.

**4. Analyzing "Yacc grep":**

For the sentence "Yacc grep," determine the most probable part-of-speech sequence using brute-force evaluation of all potential sequences. Choose the sequence with the highest probability:
- Noun Verb.
Transcribed Image Text:**Understanding a Simple Markov Model in Linguistics** A special human language is composed exclusively of nouns and verbs. A sentence begins with a noun with a 75% probability and with a verb at 25%. If a given word is a noun, there is a 75% likelihood the next word will be a verb, and a 25% chance it will be a noun. If a given word is a verb, there's a 75% chance the next word will be a noun and a 25% chance it will be a verb. This language can be modeled using a Markov chain with two states: noun and verb. **1. Markov Chain Practice:** When drawing the Markov chain for this language, it should feature: - Only two nodes and four directed edges. - Each nodal transition, such as from "noun" to "verb", will have a weight of 0.75, while "verb" to "noun" also carries a weight of 0.75. **2. Probability of Initial Sentence Structure:** Calculate the probability that the first three words of a sentence are all nouns: - Approximately 4.69%. **3. Determining the Third Word's Part of Speech:** Identify the probability that the third word in a sentence is a noun: - 25% chance. **4. Analyzing "Yacc grep":** For the sentence "Yacc grep," determine the most probable part-of-speech sequence using brute-force evaluation of all potential sequences. Choose the sequence with the highest probability: - Noun Verb.
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