Homework Help is Here – Start Your Trial Now!
Math
Probability
3. In a simple healthy-sick model without recovery transition, a patient spends an average ten years in healthy state before getting sick or die. While the expected remaining lifetime of a sick-patient is five years. In the absence of recovery transition, the probability that a patient moves from healthy state to sick is 60% of chance. (a) Use a continuous-time homogeneous Markov chain X = {X₁, t≥ 0} for analysis of such model. State the required assumptions and draw the transition diagram. (b) On recalling that the probability лi; of making a jump between two states i and j is = qij/qi, derive the intensity matrix of the Markov chain. Піј = (c) Use the Kolmogorov equation (1) to find the transition probability PHD(t) = P(X₁ = D|X0 = H) of an healthy patient would survive for t≥ 0 period of time. (d) Find the expected lifetime of an healthy patient. =

3. In a simple healthy-sick model without recovery transition, a patient spends an average ten years in healthy state before getting sick or die. While the expected remaining lifetime of a sick-patient is five years. In the absence of recovery transition, the probability that a patient moves from healthy state to sick is 60% of chance. (a) Use a continuous-time homogeneous Markov chain X = {X₁, t≥ 0} for analysis of such model. State the required assumptions and draw the transition diagram. (b) On recalling that the probability лi; of making a jump between two states i and j is = qij/qi, derive the intensity matrix of the Markov chain. Піј = (c) Use the Kolmogorov equation (1) to find the transition probability PHD(t) = P(X₁ = D|X0 = H) of an healthy patient would survive for t≥ 0 period of time. (d) Find the expected lifetime of an healthy patient. =

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question

Please do question 3c with full working out. I'm struggling to understand what to write

3. In a simple healthy-sick model without recovery transition, a patient spends an average ten years in healthy state before getting sick or die. While the expected remaining lifetime of a sick-patient is five years. In the absence of recovery transition, the probability that a patient moves from healthy state to sick is 60% of chance. (a) Use a continuous-time homogeneous Markov chain X = {X₁, t≥ 0} for analysis of such model. State the required assumptions and draw the transition diagram. (b) On recalling that the probability лi; of making a jump between two states i and j is = qij/qi, derive the intensity matrix of the Markov chain. Піј = (c) Use the Kolmogorov equation (1) to find the transition probability PHD(t) = P(X₁ = D|X0 = H) of an healthy patient would survive for t≥ 0 period of time. (d) Find the expected lifetime of an healthy patient. =
Transcribed Image Text:3. In a simple healthy-sick model without recovery transition, a patient spends an average ten years in healthy state before getting sick or die. While the expected remaining lifetime of a sick-patient is five years. In the absence of recovery transition, the probability that a patient moves from healthy state to sick is 60% of chance. (a) Use a continuous-time homogeneous Markov chain X = {X₁, t≥ 0} for analysis of such model. State the required assumptions and draw the transition diagram. (b) On recalling that the probability лi; of making a jump between two states i and j is = qij/qi, derive the intensity matrix of the Markov chain. Піј = (c) Use the Kolmogorov equation (1) to find the transition probability PHD(t) = P(X₁ = D|X0 = H) of an healthy patient would survive for t≥ 0 period of time. (d) Find the expected lifetime of an healthy patient. =
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer