The 4 × 4 stochastic matrix, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

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Answer 1

Question

Chapter 8.1, Problem 36E

(a)

To determine

To calculate: The 4×4 stochastic matrix, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

(b)

To determine

To calculate: The percent of the children’s who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

(c)

To determine

To calculate: The percent of the grandchildren of the current generation who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

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show that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say? find v42 so that v4 = ( 2/5, v42, 1)⊤ is an eigenvector of M4 with corresp. eigenvalue λ4 = 45

Answer 2

Question

Chapter 8.1, Problem 36E

(a)

To determine

To calculate: The 4×4 stochastic matrix, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

(b)

To determine

To calculate: The percent of the children’s who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

(c)

To determine

To calculate: The percent of the grandchildren of the current generation who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

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Answer 3

Question

Chapter 8.1, Problem 36E

(a)

To determine

To calculate: The 4×4 stochastic matrix, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

(b)

To determine

To calculate: The percent of the children’s who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

(c)

To determine

To calculate: The percent of the grandchildren of the current generation who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

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Answer 4

Question

Chapter 8.1, Problem 36E

(a)

To determine

To calculate: The 4×4 stochastic matrix, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

(b)

To determine

To calculate: The percent of the children’s who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

(c)

To determine

To calculate: The percent of the grandchildren of the current generation who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

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Answer 5

Chapter 8.1, Problem 36E

(a)

To determine

To calculate: The 4×4 stochastic matrix, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

(b)

To determine

To calculate: The percent of the children’s who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

(c)

To determine

To calculate: The percent of the grandchildren of the current generation who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

Answer 6

Chapter 8.1, Problem 36E

(a)

To determine

To calculate: The 4×4 stochastic matrix, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

Answer 7

Chapter 8.1, Problem 36E

(a)

To determine

To calculate: The 4×4 stochastic matrix, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

Answer 8

(b)

To determine

To calculate: The percent of the children’s who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

Answer 9

(b)

To determine

To calculate: The percent of the children’s who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

Answer 10

(c)

To determine

To calculate: The percent of the grandchildren of the current generation who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

Answer 11

(c)

To determine

To calculate: The percent of the grandchildren of the current generation who will be professionals, if a study of occupational mobility in a certain community classified occupations as P(professional), WC(white dollar), SM(skilled manual) and UM(unskilled manual), where 4% of adults are P, 20% are WC, 40% are SM and 36% are UM and the study predicts that the children of P parents, 40% becomes P, 45% becomes WC, 10% SM and 5% becomes UM, for parents of WC children’s, 20% becomes P, 60% becomes WC, 10% becomes SM and 10% becomes UM, for parents of SM children’s, 10% becomes P, 45% becomes WC, 30% becomes SM, and 15% becomes UM, for parents of UM children’s, 5% becomes P, 15% becomes WC, 25% becomes SM and 55% becomes UM.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 8.1 - 1. Is a stochastic matrix? Ch. 8.1 - 2. Learning Process An elementary learning process...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 7–12, write a stochastic matrix...Ch. 8.1 - Prob. 8E

Solution Summary: The author calculates the 4times 4 stochastic matrix for occupational mobility in a certain community classified occupations.

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