Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | Agustus 2023 |
| Nomor Soal | : | 8 |
SOAL
Diberikan sebuah fungsi survival ${S_0}\left( t \right)$ sebagai berikut:
i. \({S_0}\left( t \right) = 1;\;\) \(0 \le t < 1\)
ii. \({S_0}\left( t \right) = 1 – \;\frac{{{e^t}}}{{100}};\) \(1 \le t < 4,5\)
iii. \({S_0}\left( t \right) = 0;\;\) \(4,5 \le t\)
Hitunglah \({\mu _4}\)
a. 0,45
b. 0,55
c. 0,80
d. 1,00
e. 1,20
| Diketahui | i. \({S_0}\left( t \right) = 1;\;\) \(0 \le t < 1\) ii. \({S_0}\left( t \right) = 1 – \;\frac{{{e^t}}}{{100}};\) \(1 \le t < 4,5\) iii. \({S_0}\left( t \right) = 0;\;\) \(4,5 \le t\) |
| Rumus yang digunakan | Formula,
\({\mu _t} = – \frac{d}{{dt}}\ln [{S_0}\left( t \right)] = \) \(– \;\frac{1}{{{S_0}\left( t \right)}}\;.\;\frac{d}{{dt}}{S_0}\left( t \right)\) |
| Proses pengerjaan | \({\mu _4} = – \;\frac{1}{{1 – \frac{{\exp \left( 4 \right)}}{{100}}}}\;.\;\frac{d}{{dt}}\left[ {1 – \frac{{\exp \left( 4 \right)}}{{100}}} \right]\)
\({\mu _4} = \;\frac{{100}}{{100 – \exp \left( 4 \right)}}\;.\;\left[ {\frac{{\exp \left( 4 \right)}}{{100}}} \right]\)
\({\mu _4} = \;1,2026\; \cong 1,20\) |
| Jawaban | e. 1,20 |
