A company offers health insurance to its employees. The
insurance pays continuous premiums at the rate of $12,000/year
whenever the employee is sick, and nothing otherwise. Suppose that
a typical employee gets sick on average every 4 months ,and when
sick remains so for an average of 1/2-months. The company
constructs an appropriate continuous-time Markov chain to model
this situation.
(a) Suppose an employee is healthy today. Find the total
expected benefits that she will receive over the next year.