Complete the following life table:-
$x$ $l_{x}$ $d_{x}$ $q_{x}$ $p_{x}$ $L_{x}$
$4$ $9100$ $60$ $?$ $?$ $?$
$5$ $?$ $45$ $?$ $?$

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Solution

$d_{x} = l_{x} - l_{x + 1}$
$d_{5} = l_{4} - l_{5} ⟹ 9100 - l_{5} = 45 ⟹ l_{5} = 9055$
$d_{x} = l_{x} q_{x} ⟹ q_{4} = \frac{d_{4}}{l_{4}} = \frac{60}{9100} = \frac{3}{455} = 0.0066$
$q_{5} = \frac{d_{5}}{l_{5}} = \frac{45}{9055} = 0.005$
$p_{x} = \frac{l_{x + 1}}{l_{x}} ⟹ p_{4} = 0.995, p_{5} = 0$
$L_{x} = log p_{x} ⟹ L_{4} = log p_{4} = l o g (0.995) = - 0.0022$
$x$ $l_{x}$ $d_{x}$ $q_{x}$ $p_{x}$ $L_{x}$
$4$ $9100$ $60$ $0.0066$ $0.995$ $- 0.0022$
$5$ $9055$ $45$ $0.005$ $0$

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