8. Suppose people in a certain community are classified as being low income, middle income, or high income. Suppose further that the probabilities for children being in a given state depends on which state their parents were in according to the Markov chain transition matrix below. Income level Income level of children of parents L Low Middle High 0.15 0.6 0.25 0.15 0.35 0.5 0 0.2 0.8 M H a. If the initial distribution probabilities of families in a certain population are [.7 the distribution for the next three generations. .2 .1], find b. Find the steady-state vector for the distribution of families by income level