Question

A problem of interest to sociologists is to determine the proportion of society that has an upper-, middle- or lower-class occupation. A study across generations (from one generation to the next in same family) was conducted in United Kingdom after World War II. Three occupational classes were identified: (1) Upper-class (executives, managerial, high administrative, professionals). (2) Middle-class (high grade supervisors, non-manual, skilled manual). (3) Lower-class (semi-skilled, unskilled). Assume that transitions between social classes of the successive generations in a family can be regarded as transitions of a Markov chain (that is, the occupation of a child depends only on his or her parent’s occupation). Suppose that the transition probability matrix (from parent to child) is given by 1 2 3 1 [ 0.45 0.48 0.07 ] P = 2 [ 0.05 0.70 0.25 ] 3 [ 0.01 0.50 0.49 ] Select from the drop-down lists for the following questions. a) What is the probability that the child of a lower-class worker will attain a middle-class occupation? Ans = b) What is the probability that the grandchild of an upper-class worker will attain a middle-class occupation? Ans = c) Suppose that the proportions of the upper-, middle-, and lower-classes are 12.5%, 62.5%, 25% respectively in a given generation (initially). In the next generation, what proportion of people will be in lower-class jobs? Ans =

          A problem of interest to sociologists is to determine the proportion of society that has an upper-, middle- or lower-class occupation. A study across generations (from one generation to the next in same family) was conducted in United Kingdom after World War II. Three occupational classes were identified:
(1) Upper-class (executives, managerial, high administrative, professionals).
(2) Middle-class (high grade supervisors, non-manual, skilled manual).
(3) Lower-class (semi-skilled, unskilled).
Assume that transitions between social classes of the successive generations in a family can be regarded as transitions of a Markov chain (that is, the occupation of a child depends only on his or her parent’s occupation). Suppose that the transition probability matrix (from parent to child) is given by
1 2 3
1 [ 0.45 0.48 0.07 ]
P = 2 [ 0.05 0.70 0.25 ]
3 [ 0.01 0.50 0.49 ]
Select from the drop-down lists for the following questions.
a) What is the probability that the child of a lower-class worker will attain a middle-class occupation? Ans =
b) What is the probability that the grandchild of an upper-class worker will attain a middle-class occupation? Ans =
c) Suppose that the proportions of the upper-, middle-, and lower-classes are 12.5%, 62.5%, 25% respectively in a given generation (initially). In the next generation, what proportion of people will be in lower-class jobs? Ans =

A problem of interest to sociologists is to determine the proportion of society that has an upper-, middle- or lower-class occupation. A study across generations (from one generation to the next in same family) was conducted in United Kingdom after World War II. Three occupational classes were identified:
(1) Upper-class (executives, managerial, high administrative, professionals).
(2) Middle-class (high grade supervisors, non-manual, skilled manual).
(3) Lower-class (semi-skilled, unskilled).
Assume that transitions between social classes of the successive generations in a family can be regarded as transitions of a Markov chain (that is, the occupation of a child depends only on his or her parent’s occupation). Suppose that the transition probability matrix (from parent to child) is given by
1 2 3
1 [ 0.45 0.48 0.07 ]
P = 2 [ 0.05 0.70 0.25 ]
3 [ 0.01 0.50 0.49 ]
Select from the drop-down lists for the following questions.
a) What is the probability that the child of a lower-class worker will attain a middle-class occupation? Ans =
b) What is the probability that the grandchild of an upper-class worker will attain a middle-class occupation? Ans =
c) Suppose that the proportions of the upper-, middle-, and lower-classes are 12.5%, 62.5%, 25% respectively in a given generation (initially). In the next generation, what proportion of people will be in lower-class jobs? Ans =

Added by April C.

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