CM1 Chapter 24 relations between dependent and independent probability of decrement

Discussion in 'CM1' started by yuli2513, Aug 24, 2021.

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  1. yuli2513

    yuli2513 Very Active Member

    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?
     
    yuli2513, Aug 24, 2021
    #1
  2. Joe Hook

    Joe Hook ActEd Tutor Staff Member

    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
     
    Joe Hook, Aug 24, 2021
    #2
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  3. yuli2513

    yuli2513 Very Active Member

    Clear, thanks a lot!
     
    yuli2513, Aug 25, 2021
    #3

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