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 × 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

Use the matrices in parts (b) and (c) to find the distribution matrices for 2018 and 2019?