Exercise 2

Suppose that income from occupation of a child, as an adult, depends upon the income from the occupation of his or her parents given by the following transition matrix, where
L= low income, M= middle income, U= High income

$$\begin{array}{r} \mbox{Parents income } \\ \end{array}$$

$$\begin{array}{rrrrr} \mbox{L} & \mbox{M} &\mbox{H} \\ \end{array}$$

$$\begin{array}{r} \mbox{ Chiled's}\\ \mbox{income}\\ \mbo... ...gin{array}{r} \mbox{L}\\ \mbox{M}\\ \mbox{H}\\ \end{array}$$

a) What is the probability that the grandchild of a family of low income to be in high income level?
b) In long run, what portion of the population will be in low income level?