Hi Anyone know how to explain why if mortality follows contant force of mu over all ages, the complete expectation of life at any age is the same? Eg: if mu = 0.02, then eO_0 or eO_25 is equal to 1/0.02 = 50 years.
Just derive a formula for complete expectation based on µ: it doesn't have x in it if µ is constant, so the result is independent of x.
Is it because under constant force, your mu is the same at all ages, therefore the 'hazard' is the same, which then leads to the same expected future lifetime of individual of any age to be the same?
Yes: it's like the time till the next jump in a Poisson process (it doesn't matter how long you've been in a state, the time till you get out is unaffected by history).
