• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

Constant force & complete expectation of life

J

jensen

Member
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).
 
Back
Top