Quick question, I'm following the explanation in ASET for this question and my initial approach was WAY off, however when I compare the end result they're virtually identical (i.e. diff of 0.00001 for a dependent probability). My approach was to evaluate mu(a) @ X = 40, add that to mu(b) of 0.03. Get the survival probability, then the cumulative decrement probability. Then apportion the decrement probability as a proportion of mu(a)/[mu(a) + mu(b)]. I get 0.029345 vs 0.02934 in ASET. Is my approach in correct? I ask as it took me under a minute to calculate for a 7 mark question, with virtually identical answers. That time savings would be precious for Monday's exam. Thanks.
Hi, If I'm understanding your approach correctly you've assumed that mu(a) = 1/70. However, the question does not indicate that mu(a) is a constant and so we should assume that it's a continuous function and varies over the year i.e. it moves linearly with age from 1/70 at age 40 to 1/69 at age 41. Therefore, we need to use an integral approach rather than the approach you've outlined which is it to be used in the case of constant forces of interest. The examiners report noted that a number of students assumed that mu(a) was a constant and that this did give a very similar answer (as you've noted). It was given some but not full credit. The number of marks available in the question was obviously a red flag you might have oversimplified this question. If the number of marks for a question seems too good to be true then, unfortunately, it probably is. Hope it goes well on Monday and Tuesday.
