Chapter 8.1, Problem 30E

Student Residences According to the Higher Education Research Institute, 80% of students at baccalaureate-granting colleges who entered college in 2015 lived in College residence halls, 15% lived with Family, and 5% lived in Other types of housing. Suppose that each year, these students changed their residences as described by the following matrix. (Source: The American Freshman: National Norms Fall 2015.)

$\begin{array}{l}\underset{\_}{\text{From residence:}}\\ \begin{array}{ccc}\text{ C}& \text{F}& \text{O}\end{array}\\ \text{To residence:}|\begin{array}{c}\text{C}\\ \text{F}\\ \text{O}\end{array}\left[\begin{array}{ccc}.9& .1& .2\\ .05& .8& .1\\ .05& .1& .7\end{array}\right]\end{array}$

a. What percentage of the students who lived with family as freshmen lived in college residence halls as sophomores?

b Explain the meaning of the .8 appearing in the center of the matrix.

c. Draw the transition diagram for this Markov process.

d. What percentage of the students lived in college residence halls as sophomores? As juniors?