A life at age 50 is subject to an extra hazard during year of age 50 to 51. If the standard probability of death from age 50 to 51 is 0.006, and if the extra risk may be expressed by an addition to the standard force of mortality that decreases uniformly from 0.03 at the beginning of year to 0 at the end of the year, calculate the probability that the life will survive to age 51.
I know the formula you use is nPx = e^(- integral from 0 to n of µ(x+s) ds)
But how do you factor in the additional hazard?
Thanks!