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. =

I am not quite sure what you did in this question even though the answer is right. Is it possible to use a pen instead of typing ? That can be a great help. Thanks.

I did not understand how you have computed? Can you please briefly explain?

can you please answser part iv to this question