Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | November 2016 |
| Nomor Soal | : | 8 |
SOAL
Diketahui force of mortality
\({\mu _X} = \left\{ {\begin{array}{*{20}{c}} {0.01,\_untuk\_0 < x \le 30}\\ {0.02,\_untuk\_x > 30{\rm{ }}} \end{array}} \right.{\rm{ }}\)
Hitunglah \(_{20}{P_{20}}\)
- 0,05
- 0,238
- 0,568
- 0,741
- 0,867
| Diketahui | \({\mu _X} = \left\{ {\begin{array}{*{20}{c}} {0.01,\_untuk\_0 < x \le 30}\\ {0.02,\_untuk\_x > 30{\rm{ }}} \end{array}} \right.{\rm{ }}\) |
| Rumus yang digunakan | \(_n{P_x} = \exp ( – \int\limits_x^{x + n} {{\mu _x}} dx)\) |
| Proses pengerjaan | \(_{20}{P_{20}} = \exp ( – \int\limits_{20}^{40} {{\mu _x}{\rm{ }}} dx)\)
\(= \exp ( – (\int\limits_{20}^{30} {{\mu _x}{\rm{ }}} dx + \int\limits_{30}^{40} {{\mu _x}{\rm{ }}} dx)\)
\(= \exp ( – (\int\limits_{20}^{30} {0.01{\rm{ }}} dx + \int\limits_{30}^{40} {{\rm{0}}{\rm{.02 }}} dx)\)
\(= 0.74082\)
\(= 0.741\) |
| Jawaban | d. 0,741 |
