Home /
Expert Answers /
Statistics and Probability /
q2-consider-a-disability-model-with-three-states-healthy-h-disabled-di-and-dead-de-the-tr-pa303

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.)