Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
November 2015 |
| Nomor Soal |
: |
8 |
SOAL
Jika diketahui \(q_x^{‘\left( d \right)} = 0,2\) dan \(q_x^{‘\left( w \right)} = 0,4\). Hitunglah \(q_x^{\left( \tau \right)}\)
- 0,08
- 0,32
- 0,12
- 0,92
- 0,52
| Diketahui |
\(q_x^{‘\left( d \right)} = 0,2\) dan \(q_x^{‘\left( w \right)} = 0,4\) |
| Rumus yang digunakan |
\(q_x^{\left( d \right)} = q_x^{‘\left( d \right)}\left( {1 – \frac{1}{2}q_x^{‘\left( w \right)}} \right){\rm{ }}\) dan \(q_x^{\left( w \right)} = q_x^{‘\left( w \right)}\left( {1 – \frac{1}{2}q_x^{‘\left( d \right)}} \right)\)
\(q_x^{\left( \tau \right)} = q_x^{\left( d \right)} + q_x^{\left( w \right)}\) |
| Proses pengerjaan |
\(q_x^{\left( d \right)} = q_x^{‘\left( d \right)}\left( {1 – \frac{1}{2}q_x^{‘\left( w \right)}} \right)\)
\(= 0,2\left( {1 – \frac{{0,4}}{2}} \right)\)
\(= 0,16\) |
| \(q_x^{\left( w \right)} = q_x^{‘\left( w \right)}\left( {1 – \frac{1}{2}q_x^{‘\left( d \right)}} \right)\)
\(= 0,4\left( {1 – \frac{{0,2}}{2}} \right)\)
\(= 0,36\) |
| \(q_x^{\left( \tau \right)} = q_x^{\left( d \right)} + q_x^{\left( w \right)}\)
\(= 0,16 + 0,36\)
\(= 0,52\) |
| Jawaban |
e. 0,52 |
