In a given population, the probabilities of dying in successive 10-year intervals, in percent, are [6, 4, 4, 4, 4, 8, 15, 20, 40, 100]. Assume that total deaths in each interval occur evenly throughout the interval.

i) Find the proportion of individuals in this population who survive to the end of each 10-year interval. Also find the approximate life expectancies in this population at birth, and at age 60.

Now suppose that there are two diseases that may affect the quality of life of individuals in this population. On their sixtieth birthday, surviving individuals (that is, those surviving to the end of interval 6) face a 10% risk of getting disease A, from which they will never recover, and which reduces the quality of their remaining life by 40% (but does not change their risk of dying). On their seventieth birthday, survivors who don’t already suffer from A also face a 10 % risk of getting it, with the same consequences. Moreover, there is another disease, B, which, at any given time, afflicts 25% of all those in their 70s, 80s, and 90s, and which reduces the sufferer’s quality of life by 30% but does not change their risk of dying.

ii) Calculate the fractions of this population who will suffer from disease A in the last four age intervals. Assuming that a person can have both A and B, and that the probabilities of the two kinds of illness are independent, also calculate what proportions in these age brackets will have both A and B