The victims of a certain disease being treated at Wake Medical
Center are classified annually as follows: cured,
in temporary remission, sick, or
dead from the disease. Once a patient is cured, he
is permanently immune. Each year, those in remission get sick again
with probability 0.05, are cured with probability 0.3, 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 the following questions. (Give your answers correct to three
decimal places.)
(a) If a patient is now in remission, what is the probability he
is still alive in two years? (Hint: In which states is a patient
alive?)
(b) If a patient is now in remission, what is the probability he
dies within three years?
(c) On average, how many years will a patient in remission live
before being cured or dying from the disease?
(d) If a patient is presently sick, what is the expected number of
years before the patient is cured or dies?
(e) What is the probability that someone who is currently in
remission will eventually be cured?
(f) What is the probability that someone who is currently sick will
eventually be cured?
