2. Individuals are classified by income as lower-class (L), middle-class (M), or

Question

2. Individuals are classified by income as lower-class (L), middle-class (M), or upper-class (U). It is asserted that the income class of an individual is mainly determined by the income Class of his parents ata on 1,000 individuals is available to study change in income class from one generation to the next 220 from L class, 650 from M, and 130 from U. The individuals from L class had the following offsprings: 327 in L class, 137 in M, and 63 in U. The individuals from M class had 158 offsprings in L class, 156 in M, and 215 in U. The individuals from U class had 19 offsprings in L class, 59 in M, and 96 in U. Use Markov chains based analysis to answer the following questions. a) Find the probability that a L-class person will have a U-class grandchild. Compare it to the probability that a

Explanation / Answer

From the given data we get the probability distribution table as below:

L

0.22

M

0.65

U

0.13

Total =

1

There are 1000 individuals, we multiply this value with different probabilities and find the following frequency table.

0.22 * 1000 = 220

0.65 * 1000 = 650

0.13 * 1000 = 130

L

220

M

650

U

130

Total =

1000

L

0.22

M

0.65

U

0.13

Total =

1

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