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 |