Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | November 2015 |
| Nomor Soal | : | 9 |
SOAL
Jika \(\mu _{50 + t}^{\left( d \right)}\) dan \(\mu _{50 + t}^{\left( w \right)}\) bernilai konstan pada \(0 < t < 1\), hitunglah \(q_{60}^{\left( d \right)}\) jika diketahui \(q_{60}^{‘\left( d \right)} = q_{60}^{‘\left( w \right)} = 0,3\)
- 0,180
- 0,342
- 0,255
- 0,168
- 0,088
| Diketahui | \(\mu _{70 + t}^{\left( d \right)}\) dan \(\mu _{70 + t}^{\left( w \right)}\) adalah konstan pada \(0 < t < 1\) dan \(q_{70}^{‘\left( d \right)} = q_{70}^{‘\left( w \right)} = 0,3\) |
| Rumus yang digunakan | \(q_x^{\left( d \right)} = q_x^{‘\left( d \right)}\left( {1 – \frac{1}{2}q_x^{‘\left( w \right)}} \right)\) |
| Proses pengerjaan | \(q_x^{\left( d \right)} = q_x^{‘\left( d \right)}\left( {1 – \frac{1}{2}q_x^{‘\left( w \right)}} \right)\)
\(= 0,3\left( {1 – \frac{{0,3}}{2}} \right)\)
\(= 0,255\) |
| Jawaban | c. 0,255 |
