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  • A confusing conceptual question

    I doubt the answer to Course 3,Fall 2004 #4:

    Here is the problem: For a population which contains equal numbers of males and females at birth
    (i) for male, force of mortality u1(x) = 0.1 ;
    (ii) for female, force of mortality u2(x) = 0.08.
    Calculate q(60)=?


    My answer is:

    P(60)= {P(60)|[it is male]} X Pr[it is male] + {P(60) | [it is female]} X Pr[it is female] = {exp( - 0.1X60 )} X 0.5 + {exp ( -0.08X60)}X0.5=0.914 ; Then q(60)=1-p(60) = 0.086

    While the "right" answer shows:

    S(61)={S(61)|[it is male]} X Pr[it is male] + {S(61) | [it is female]} X Pr[it is female] = {exp( - 0.1X61 )} X 0.5 + {exp ( -0.08X61)}X0.5=0.00492

    S(60)={S(60)|[it is male]} X Pr[it is male] + {S(60) | [it is female]} X Pr[it is female] = {exp( - 0.1X60 )} X 0.5 + {exp ( -0.08X60)}X0.5=0.005354

    then q(60)=1-P(60)=0.081


    I am very confused why my method is not right? Does it really make difference if I condition directly on P(60) instead of condition on S(60)?

    I would greatly appreciate if anybody could give me clues.

  • #2
    Originally posted by charles2002chen
    I doubt the answer to Course 3,Fall 2004 #4:

    Here is the problem: For a population which contains equal numbers of males and females at birth
    (i) for male, force of mortality u1(x) = 0.1 ;
    (ii) for female, force of mortality u2(x) = 0.08.
    Calculate q(60)=?


    My answer is:

    P(60)= {P(60)|[it is male]} X Pr[it is male] + {P(60) | [it is female]} X Pr[it is female] = {exp( - 0.1X60 )} X 0.5 + {exp ( -0.08X60)}X0.5=0.914 ; Then q(60)=1-p(60) = 0.086

    While the "right" answer shows:

    S(61)={S(61)|[it is male]} X Pr[it is male] + {S(61) | [it is female]} X Pr[it is female] = {exp( - 0.1X61 )} X 0.5 + {exp ( -0.08X61)}X0.5=0.00492

    S(60)={S(60)|[it is male]} X Pr[it is male] + {S(60) | [it is female]} X Pr[it is female] = {exp( - 0.1X60 )} X 0.5 + {exp ( -0.08X60)}X0.5=0.005354

    then q(60)=1-P(60)=0.081


    I am very confused why my method is not right? Does it really make difference if I condition directly on P(60) instead of condition on S(60)?

    I would greatly appreciate if anybody could give me clues.
    Your "P(60)" is the probability that you survive to 60, given that you're considering newborns. In actuality, your P(60) = 60_p_0 This is partially right, except that p_60 is translated as "the probability of surviving to 61, given that the person is age 60." So, yes - you need the probability of surviving to age 61, and condition on surviving to age 60, which is what S(61) / S(60) is.

    Comment


    • #3
      Originally posted by charles2002chen
      I doubt the answer to Course 3,Fall 2004 #4:
      ...
      I would greatly appreciate if anybody could give me clues.
      And for the record, you can always post the problem in the appropriate exam thread, so that others can see the problem and answer it, or benefit from the help on the problem.

      Comment


      • #4
        Wat, thanks a lot for your help.

        Comment

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