Chapter 8.1, Problem 22E

Health Plan Option A university faculty health plan offers an optional dental plan. During the open enrollment period each year, 90% of the people who currently have the dental plan reenroll for it and 10% opt out. Of the people who do not have the dental plan, 40% enroll for it and 60% stay out of the plan.

a. Draw a transition diagram with ovals labeled “Dental plan” and “No dental plan” for this Markov process.

b. Set up the $2\times 2$ stochastic matrix (with columns and rows labeled D and N) for the Markov process.

c. Compute the second power of the matrix in part (b).

d. Suppose that, for the year 2017, 70% of the faculty were in the dental plan and 30% were not in the plan. That is, the initial distribution is given by the column matrix $\left[\begin{array}{l}.7\\ .3\end{array}\right]$. Use the matrices in parts (b) and (c) to find the distribution matrices for 2018 and 2019.