Answered: The victims of a certain disease being…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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?
years

(d) If a patient is presently sick, what is the expected number of years before the patient is cured or dies?
years

(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?

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