Suppose a man's occupation can be classified as professional, skilled worker, or unskilled worker. Suppose eighty percent of the sons of professional men are professionals, ten percent skilled workers, and ten percent unskilled workers. further suppose that sixty percent of the sons of skilled workers are skilled workers, twenty percent professional, and twenty percent unskilled. finally, in the case of unskilled workers, fifty percent of the sons are unskilled workers and twenty-five percent are in the other two categories. Assume each man has at least one son, and construct a Markov chain by tracing the occupation of a randomly selected son of a particular family over several generations. Construct the transition probabilities matrix. Find the probability that the randomly selected grandchild of an unskilled worker is a professional worker.
Suppose a man's occupation can be classified as professional, skilled worker, or unskilled worker. Suppose eighty percent of the sons of professional men are professionals, ten percent skilled workers, and ten percent unskilled workers. further suppose that sixty percent of the sons of skilled workers are skilled workers, twenty percent professional, and twenty percent unskilled. finally, in the case of unskilled workers, fifty percent of the sons are unskilled workers and twenty-five percent are in the other two categories. Assume each man has at least one son, and construct a Markov chain by tracing the occupation of a randomly selected son of a particular family over several generations. Construct the transition probabilities matrix. Find the probability that the randomly selected grandchild of an unskilled worker is a professional worker.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 26PPS
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Suppose a man's occupation can be classified as professional, skilled worker, or unskilled worker.
Suppose eighty percent of the sons of professional men are professionals, ten percent skilled workers, and ten percent unskilled workers.
further suppose that sixty percent of the sons of skilled workers are skilled workers, twenty percent professional, and twenty percent unskilled.
finally, in the case of unskilled workers, fifty percent of the sons are unskilled workers and twenty-five percent are in the other two categories.
Assume each man has at least one son, and construct a Markov chain by tracing the occupation of a randomly selected son of a particular family over several generations. Construct the transition probabilities matrix.
Find the probability that the randomly selected grandchild of an unskilled worker is a professional worker.
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