Thread: pdf of future lifetime

fT(x)(t) = 2e^(-2t) , t ≥ 0

find
a) °ex (the ° is supposed to be above the e)
b) Var[T(x)]
c) m(x), median future lifetime
d) mx, central death rate at age x

is this the right track for part a.

°ex = E[T(x)] = ∫ (from 0 to infin) tp1 dt