Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | Mei 2018 |
| Nomor Soal | : | 14 |
SOAL
Diberikan
- Kematian menyebar secara seragam pada tiap usia
- \({\mu _{45.5}} = 0.3\)
Hitunglah \(e_{45:\left. {\overline {\, 1 \,}}\! \right| }^o\)
- 0,8624
- 0,8712
- 0,8813
- 0,8945
- 0,9001
| Diketahui | Kematian menyebar seragam (UUD)
\({\mu _{45.5}} = 0.3\) |
| Rumus yang digunakan | \(e_{x:\left. {\overline {\, 1 \,}}\! \right| }^o = {p_x} + \frac{1}{2}{q_x}\)
\({\mu _{x + \frac{1}{2}}} = \frac{{{q_x}}}{{1 – \frac{1}{2}{q_x}}}\) |
| Proses pengerjaan | \({\mu _{45.5}} = \frac{{{q_{45}}}}{{1 – \frac{1}{2}{q_{45}}}}\)
\(\Leftrightarrow (0.3)(1 – \frac{1}{2}{q_{45}}) = {q_{45}}\)
\(\Leftrightarrow 0.3 – 0.15{q_{45}} = {q_{45}}\)
\(\Leftrightarrow 0.3 = 1.15{q_{45}}\)
\(\Leftrightarrow {q_{45}} = \frac{{0.3}}{{1.15}} = 0.261{\rm{ (*)}}\)
dari (*) diperoleh
\({p_{45}} = 1 – {q_{45}} = 1 – 0.261 = 0.739\)
selanjutnya
\(e_{45:\left. {\overline {\, 1 \,}}\! \right| }^o = {p_{45}} + \frac{1}{2}{q_{45}} = 0.739 + (0.5)(0.261) = 0.8695 = 0.87\) |
| Jawaban | b. 0.8712 |
