recently I am doing 1 question
A life aged (40) is subject to an extra risk for the next year only. Suppose the normal probability of death is 0.003, and that the extra risk may be expressed by adding the function 0.03(1-t) to the normal force of mortality for this year. What is the probability of survival to age 41?
I can write the function as
and I can get
However, I am not very sure how can I integrate the μ and get the correct answer. Could you please see if there are any thing wrong on my calculation? Thank you.