Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
Mei 2018 |
| Nomor Soal |
: |
15 |
SOAL
Diberikan
- \(j(x) = {1.3^{x – 100}}\)
- \({\mu _x} = \frac{{j(x)}}{{1 + j(x)}}\)
Hitunglah \(\frac{{{q_{103}}}}{{{q_{102}}}}\)
- 1.01
- 1.02
- 1.03
- 1.04
- 1.06
| Diketahui |
- \(j(x) = {1.3^{x – 100}}\)
- \({\mu _x} = \frac{{j(x)}}{{1 + j(x)}} = \frac{{{{1.3}^{x – 100}}}}{{1 + {{1.3}^{x – 100}}}}\)
|
| Rumus yang digunakan |
\(_n{p_x} = \exp ( – \int\limits_x^{x + n} {{\mu _x}{\rm{ }}dx)} \) |
| Proses pengerjaannya |
\({p_{103}} = \exp ( – \int\limits_{103}^{104} {\frac{{{{1.3}^{x – 100}}}}{{1 + {{1.3}^{x – 100}}}}{\rm{ }}dx) = 0.48947} \)
\({p_{102}} = \exp ( – \int\limits_{102}^{103} {\frac{{{{1.3}^{x – 100}}}}{{1 + {{1.3}^{x – 100}}}}{\rm{ }}dx) = 0.51782} \)
\(\frac{{{q_{103}}}}{{{q_{102}}}} = \frac{{1 – {p_{103}}}}{{1 – {p_{102}}}} = \frac{{1 – 0.48947}}{{1 – 0.51782}} = 1.058 = 1.06\) |
| Jawaban |
e. 1.06 |
