Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
November 2014 |
| Nomor Soal |
: |
13 |
SOAL
Berdasarkan soal nomor 11. Tentukan probabilitas bahwa seorang yang berusia 10 tahun akan meninggal di antara usia 30 dan 45
- \(\frac{1}{{24}}\)
- \(\frac{1}{{12}}\)
- \(\frac{1}{8}\)
- \(\frac{1}{6}\)
- \(\frac{5}{{24}}\)
| Diketahui |
\(S\left( x \right) = \frac{{90 – x}}{{90 + x}},0 \le x \le 90\) |
| Rumus yang digunakan |
- \({}_{\left. t \right|u}{q_x} = {}_t{p_x} \cdot {}_u{q_{x + t}}\)
- \({}_t{p_x} = \frac{{S\left( {x + t} \right)}}{{S\left( x \right)}}\) dengan \({}_t{q_x} = 1 – {}_t{p_x}\)
|
| Proses pengerjaan |
\({}_{\left. {20} \right|15}{q_{10}} = {}_{20}{p_{10}} \cdot {}_{15}{q_{30}}\)
\({}_{\left. {20} \right|15}{q_{10}} = \frac{{S\left( {30} \right)}}{{S\left( {10} \right)}} \cdot \left( {1 – \frac{{S\left( {45} \right)}}{{S\left( {30} \right)}}} \right) = \frac{{S\left( {30} \right)}}{{S\left( {10} \right)}} \cdot \left( {\frac{{S\left( {30} \right) – S\left( {45} \right)}}{{S\left( {30} \right)}}} \right)\)
\({}_{\left. {20} \right|15}{q_{10}} = \frac{{S\left( {30} \right) – S\left( {45} \right)}}{{S\left( {10} \right)}}\)
\({}_{\left. {20} \right|15}{q_{10}} = \frac{{\frac{{90 – 30}}{{90 + 30}} – \frac{{90 – 45}}{{90 + 45}}}}{{\frac{{90 – 10}}{{90 + 10}}}}\)
\({}_{\left. {20} \right|15}{q_{10}} = \frac{5}{{24}}\) |
| Jawaban |
E. \(\frac{5}{{24}}\) |
