The relative income of a child (low, medium, or high) generally depends on the relative income of the child’s parents. The matrix P, given by 

is called a left stochastic transition matrix. For example, the entry P₂₁ = 0.5 means that 50% of the children of low relative income parents will transition to the medium level of income. The diagonal entry P_{i I} represents the percent of children who remain in the same income level as their parents. Assuming that the transition matrix is valid from one generation to the next, compute and interpret P².

Transcribed Image Text:

Parent's Income Н 0.2 0.1 L 0.5 M Child's income 0.4 0.5 0.6 P = 0.2 0.4 H 0.1 ||