Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Matematika Aktuaria |
| Periode Ujian | : | Juni 2015 |
| Nomor Soal | : | 24 |
SOAL
Berdasarkan soal nomor 23. Hitunglah \(e_{\overline {30:50} }^0\)
- 10
- 20
- 30
- 40
- 50
| Diketahui | - \(\left( {30} \right)\) dan \(\left( {50} \right)\) adalah suatu independent lives dengan constant force of mortality, \(\mu = 0,05\)
- \(\delta = 0,03\)
|
| Rumus yang digunakan | \(e_{\overline {xy} }^0 = e_x^0 + e_y^0 + e_{xy}^0\)
\({\mu _{xy}} = {\mu _x} + {\mu _y}\)
Untuk Distribusi Eksponensial : \(e_x^0 = \frac{1}{{{\mu _x}}}\) |
| Proses pengerjaan | \({\mu _{xy}} = {\mu _x} + {\mu _y} = 0.05 + 0.05 = 0.1\) |
| \(e_{\overline {xy} }^0 = e_x^0 + e_y^0 + e_{xy}^0\)
\(e_{\overline {xy} }^0 = \frac{1}{{{\mu _x}}} + \frac{1}{{{\mu _y}}} + \frac{1}{{{\mu _{xy}}}}\)
\(e_{\overline {xy} }^0 = \frac{1}{{0.05}} + \frac{1}{{0.05}} + \frac{1}{{0.1}}\)
\(e_{\overline {xy} }^0 = 20 + 20 + 10 = 50\) |
| Jawaban | c. 30 |
