Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Matematika Aktuaria |
| Periode Ujian | : | Juni 2015 |
| Nomor Soal | : | 25 |
SOAL
Berdasarkan soal nomor 23. Hitunglah \(Var\left[ {{T_{30:50}}} \right]\)
- 50
- 100
- 150
- 200
- 400
| 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 | \({\mu _{xy}} = {\mu _x} + {\mu _y}\)
Untuk Distribusi Eksponensial :
Mean: \(E\left[ {{T_{xy}}} \right] = e_{xy}^0 = \frac{1}{{{\mu _{xy}}}}\)
Varians: \(Var\left[ {{T_{xy}}} \right] = {\left( {\frac{1}{{{\mu _{xy}}}}} \right)^2}\) |
| Proses pengerjaan | \(Var\left[ {{T_{30:50}}} \right] = {\left( {\frac{1}{{{\mu _{xy}}}}} \right)^2} = {\left( {\frac{1}{{{\mu _x} + {\mu _y}}}} \right)^2} = {\left( {\frac{1}{{0.05 + 0.05}}} \right)^2} = 100\) |
| Jawaban | b. 100 |
