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 |