# (Solved): Q2 Consider a disability model with three states: Healthy (H), Disabled (DI), and Dead (DE). The tr ...

Q2 Consider a disability model with three states: Healthy

(H)

, Disabled (DI), and Dead (DE). The transi- tions between these states are governed by a non-homogeneous continuous-time Markov chain. The transition rates are given as follows: The rate of transitioning from H to DI at time

t

is

\lambda _(H,DI)(t)=0.02+0.001t

. The rate of transitioning from DI to DE at time

t

is

\lambda _(DI,DE)(t)=0.03+0.002t

. The rate of transitioning from H to DE at time

t

is

\lambda _(H,DE)(t)=0.01

. There are no transitions from DI to H or from DE to any other state. (a) Write down the generator matrix

Q(t)

for this non-homogeneous continuous-time Markov chain. (b) Given that an individual is Healthy at time

t=0

, compute the probability that the individual will stay health over

0,10

. (c) Compute the probability that an individual who is disabled at time

t=0

will not be alive at time

t=10

. (d) Compute the probability that an individual who is healthy at time

t=0

will be disabled at time

t=10

. (Hint: You can use

R

if necessary.)

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