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
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
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Finite Mathematics & Its Applications Plus Mylab Math With Pearson Etext -- Title-specific Access Card Package (12th Edition)
- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.arrow_forwardIn Exercises 1-4, let P=[0.50.30.50.7] be the transition matrix for a Markov chain with two states. Let X0=[0.50.5]be the initial state vector for the population. What proportion of the state 2 population will be in state 2 after two steps?arrow_forwardConsider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show that the steady state matrix X depends on the initial state matrix X0 by finding X for each X0. X0=[0.250.250.250.25] b X0=[0.250.250.400.10] Example 7 Finding Steady State Matrices of Absorbing Markov Chains Find the steady state matrix X of each absorbing Markov chain with matrix of transition probabilities P. b.P=[0.500.200.210.300.100.400.200.11]arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning