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 |