CM1 Chapter 24 relations between dependent and independent probability of decrement

[yuli2513]

In Q24.1 (question on page 45, answer on page 51) of the chapter end practice questions, (i) states that the dependent probabilities of decrement can never exceed the corresponding independent probabilities. However, the question (a) on page 17 provides a situation where the dependent probability of sickness exceeds the corresponding independent probability.

so I am a bit confused here, is either of them wrong here?

 

[Joe Hook]

That a dependent probability can never exceed a corresponding independent probability is true. However, the equation on page 17 is not comparing like-for-like probabilities. 1p(HS) is not the independent probability of leaving the healthy state via sickness during the year but is the probability of leaving the healthy state AND then remaining in the sick state until time 1.

Can appreciate the confusion here but hopefully the above helps.

Joe

 

[yuli2513]

That a dependent probability can never exceed a corresponding independent probability is true. However, the equation on page 17 is not comparing like-for-like probabilities. 1p(HS) is not the independent probability of leaving the healthy state via sickness during the year but is the probability of leaving the healthy state AND then remaining in the sick state until time 1.

Can appreciate the confusion here but hopefully the above helps.

Joe

Clear, thanks a lot!