I am trying to find the following:
Suppose that for a population of individuals $_tp_x$ is given by:
$_tp_x=(1-\frac{t}{125-x})^{1/5}$ for $0\le t \le125-x$
Calculate the life expectancy E(Tx) for a person aged 55 from this population and the force of mortality at age 90 for an individual aged 60.
I saw that: The expected future lifetime at age $x$ is given by:
$e_x=E[T(x)]$, which is:
$$\int_{0}^{\infty} {_tp_x} dt$$
So i did:
$$\int_{0}^{125-x} (1-\frac{t}{125-x})^{1/5} dt=\frac{1}{22}*(x-125)^{2}$$
substituting $x$ by 55, I obtained:
$222.72$, which I believe that is something wrong with my calculations or formula. Can anyone help me on this?
Also can anyone give me any tip in how to find the force mortality? Or anything that I can read about it?
Thanks