Chapter 8.1, Problem 29E

Political Views According to the Higher Education Research Institute, 33% of students at baccalaureate-granting colleges who entered college in 2015 characterize their political views as Liberal, 45% as Middle-of-the-road, and 22% as Conservative. Suppose that, each year, these students changed their political views as described by the following matrix. (Source: The American Freshman: National Norms Fall 2015.)

$\begin{array}{l}\underset{\_}{\text{From view:}}\\ \begin{array}{ccc}\text{ L}& \text{M}& \text{C}\end{array}\\ \text{To view:}|\begin{array}{c}\text{L}\\ \text{M}\\ \text{C}\end{array}\left[\begin{array}{ccc}.94& .02& .01\\ .05& .96& .04\\ .01& .02& .95\end{array}\right]\end{array}$

a. What percentage of the students who held conservative political views as freshmen held middle-of-the-road views as sophomores?

b. Explain the meaning of the .96 appearing in the center of the matrix.

c. Draw the transition diagram for this Markov process.

d. What percentage of the students held middle-of-the-road political views as sophomores? As juniors?