Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
November 2016 |
| Nomor Soal |
: |
22 |
SOAL
Berdasarkan soal no 21, hitunglah probabilitas seseorang akan meninggal dunia sebelum umur 75 tahun:
- 0.078
- 0.088
- 0.095
- 0.105
- 0.118
| Diketahui |
\({\mu _x}(t) = \left\{ {\begin{array}{*{20}{c}} {0.01}\\ {0.015}\\ {0.025} \end{array}\begin{array}{*{20}{c}} {,60 < t \le 70}\\ {,70 < t \le 80}\\ {,t > 80} \end{array}} \right.\) |
| Rumus yang digunakan |
\(_t{p_x} = \exp ( – \int\limits_x^{x + t} {{u_x}(y){\rm{ }}dy} )\) |
| Proses pengerjaan |
\(_{10}{p_{65}} = \exp ( – \int\limits_{65}^{80} {{u_x}(y){\rm{ }}dy} )\)
\(= \exp \left( { – (\int\limits_{65}^{70} {0.01{\rm{ }}dy + } \int\limits_{70}^{75} {{\rm{0}}{\rm{.015 }}dy} )} \right)\)
\(= 0.882497\)
maka
\(_{75}{q_{65}} = 1{ – _{75}}{p_{65}} = 1 – 0.882497 = 0.117503 = 0.118\) |
| Jawaban |
e. 0.0118 |
