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?