The victims of a certain disease being treated at Wake Medical Center are classified annually as follows:cured, in temporaryremission,sick, ordeadfrom the disease. Once a patient is cured, he is permanently immune. Each year, those in remission get sick again with probability 0.12, are cured with probability 0.23, die with probability 0.05, and stay in remission with probability 0.6. Those who are sick are cured with probability 0.05, die with probability 0.2, go into remission with probability 0.4, and remain sick with probability 0.35.

Find the transition matrix and do the calculations necessary to answer these questions.

(a) If a patient is now in remission, what is the probability he is still alive in 2 years? (Hint: In which of the states is the patient still alive?)

(b) If a patient is now in remission, what is the probability he dies within 3 years?