Each year, employees at a company are given the option of donating to a local charity as part of a payroll deduction plan. In general, 80 percent of the employees enrolled in the plan in any one year will choose to sign up again the following year, and 30 percent of the unenrolled will choose to enroll the following year. Determine the transition matrix for the Markov process and find the steadystate vector. What percentage of employees would you expect to find enrolled in the program in the long run?

In an office complex of 1000 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 85% chance that she will be at work tomorrow, and if the employee is absent today, there is a 70% chance that she will be absent tomorrow. Suppose that today there are 740 employees at work. (A graphing calculator is recommended.) (a) Find the transition matrix A for this scenario. at work absent A = (b) Predict the number that will be at work five days from now. (Round your answer to the nearest integer.) employees (c) Find the steady-state vector x. (Round your answer to two decimal places.)

Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 90% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 50% chance that the next concert will be cancelled. What is the long-run probability that a concert will  not be cancelled? a. 1/4 b. 1/10 c. 1/6 d. 1/2 e. 5/6 f. None of the others are correct

Answer the following questions.

The weather at a seaside resort each day is classified as either Sunny or Rainy. The probability that any two consecutive days are both sunny is 0.6, with the other three combinations being equally likely. Treating the situation as a two-state Markov chain, answer the following: (a) Find the transition matrix P and the stationary distribution vector r. (b) Find the 5-step transition matrix p(5) and hence find the probability that, if it is sunny on Sunday, it will be rainy on Friday. (c) If a day is chosen at random and found to be rainy, what is the expected number of sunny days before the next rainy day?