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Q2) In a language school, the path of a student's language level has been modeled as a Markov Chain with the following transition probabilities from the lowest level (Beginner) through the highest level (Advanced): Beginner Elementary Intermediate English Upper-Intermediate Quit 0.45 Advanced Beginner Elementary Intermediate English Upper-Intermediate Quit Advanced 0.4 0.1 0.05 0.1 0.5 0.3 0.1 0.1 0.4 0.3 0.2 0.2 0.4 0.2 0.2 11 Each student's state is observed at the beginning of each semester. For instance; if a student's language level is elementary at the beginning of the semester, there is an 30% chance that she will progress to intermediate level at the beginning of next semester, a 50% chance that she will still be in the elementary level, a 10% chance that she will regress to beginner level and 10% chance that she will quit the language school. Find the probability that a student with beginner level will eventually have an advanced level. Assume beginner level is state 1, elementary is state 2 and goes on. (You can round to two decimal places. Explicitly write the values for fis i E [1,6])

Q2) In a language school, the path of a student's language level has been modeled as a Markov Chain with the following transition probabilities from the lowest level (Beginner) through the highest level (Advanced): Beginner Elementary Intermediate English Upper-Intermediate Quit 0.45 Advanced Beginner Elementary Intermediate English Upper-Intermediate Quit Advanced 0.4 0.1 0.05 0.1 0.5 0.3 0.1 0.1 0.4 0.3 0.2 0.2 0.4 0.2 0.2 11 Each student's state is observed at the beginning of each semester. For instance; if a student's language level is elementary at the beginning of the semester, there is an 30% chance that she will progress to intermediate level at the beginning of next semester, a 50% chance that she will still be in the elementary level, a 10% chance that she will regress to beginner level and 10% chance that she will quit the language school. Find the probability that a student with beginner level will eventually have an advanced level. Assume beginner level is state 1, elementary is state 2 and goes on. (You can round to two decimal places. Explicitly write the values for fis i E [1,6])

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 9EQ
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Q2) In a language school, the path of a student's language level has been modeled as a Markov Chain with the following transition probabilities from the lowest level (Beginner) through the highest level (Advanced): Beginner Elementary Intermediate English Upper-Intermediate Quit Advanced Beginner Elementary Intermediate English Upper-Intermediate 0.4 0.1 0.05 0.45 0.1 0.5 0.3 0.1 0.1 0.4 0.3 0.2 0.2 0.4 0.2 0.2 Quit 1 Advanced Each student's state is observed at the beginning of each semester. For instance; if a student's language level is elementary at the beginning of the semester, there is an 30% chance that she will progress to intermediate level at the beginning of next semester, a 50% chance that she will still be in the elementary level, a 10% chance that she will regress to beginner level and 10% chance that she will quit the language school. Find the probability that a student with beginner level will eventually have an advanced level. Assume beginner level is state 1, elementary is state 2 and goes on. (You can round to two decimal places. Explicitly write the values for fis i E [1,6])
Transcribed Image Text:Q2) In a language school, the path of a student's language level has been modeled as a Markov Chain with the following transition probabilities from the lowest level (Beginner) through the highest level (Advanced): Beginner Elementary Intermediate English Upper-Intermediate Quit Advanced Beginner Elementary Intermediate English Upper-Intermediate 0.4 0.1 0.05 0.45 0.1 0.5 0.3 0.1 0.1 0.4 0.3 0.2 0.2 0.4 0.2 0.2 Quit 1 Advanced Each student's state is observed at the beginning of each semester. For instance; if a student's language level is elementary at the beginning of the semester, there is an 30% chance that she will progress to intermediate level at the beginning of next semester, a 50% chance that she will still be in the elementary level, a 10% chance that she will regress to beginner level and 10% chance that she will quit the language school. Find the probability that a student with beginner level will eventually have an advanced level. Assume beginner level is state 1, elementary is state 2 and goes on. (You can round to two decimal places. Explicitly write the values for fis i E [1,6])
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