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