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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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