Proceeding from an heuristic argument, show that er _ 2Px(2 + ex+2). If a person survives 2 years (with probability 2pz), her/his mean curtate-future-lifetime will be 1 + ex+2. However, her/his curtate-future-lifetime will be 1 when she/he dies within 2 years. If a person dies within 2 year, her/his curtate life time will be 2, and if the person survives 2 year (with probability 2pr), her/his mean curtate life time will be ex+2 O If the person survives one year (with probability pr), her/his mean curtate life time will be 1 + er+1 O If a person survives 2 years, then, at this moment, the total (starting from the age a) expected life time equals 2+ er+2