Question

find the standard probabilities of:

1) 2.5P20

2) 2.5q20

3) 2.5/q20

Given that the force of mortality for a survival model is given by the formula:

u(x) = 0.9/90-x

Answer 1

Given u(x) =0.9/90-x

1. 2.5P20

$_{t}P_{x}=exp(-\int_x^{x+t}u_{y}dy)$

$=exp(-\int_{20}^{22.5}\frac{0.9}{90-y}dy)$

=0.9678

2. 2.5q20

$_tq_x=1-{_tp_x}$

$_{2.5}q_{20}=1-{_{2.5}p_{20}}$

=1-0.9678

=0.0322

3. 2.5/q20

$_{t|} q_x=_tp_x-_{t+1}p_x$

$_{2.5|}q_{20}=_{2.5}p_{20}-_{3.5}p_{20}$

$_{3.5}p_{20}=exp(-\int_{20}^{23.5}\frac{0.9}{90-y}dy)$

=0.9549

=0.9678-0.9549

=0.0129