Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
November 2015 |
| Nomor Soal |
: |
1 |
SOAL
Diberikan \({\mu _{35 + t}} = \frac{1}{{100 + t}}\). Hitunglah nilai dari \({}_{10}{p_{35}}\)
- \(\frac{7}{{11}}\)
- \(\frac{8}{{11}}\)
- \(\frac{9}{{11}}\)
- \(\frac{{10}}{{11}}\)
- 1
| Diketahui |
\({\mu _{35 + t}} = \frac{1}{{100 + t}}\) |
| Rumus yang digunakan |
\({}_t{p_x} = \exp \left[ { – \int\limits_0^t {{\mu _{x + s}}ds} } \right]\) |
| Proses pengerjaan |
\({{}_{10}{p_{35}} = \exp \left[ { – \int\limits_0^{10} {{\mu _{35 + s}}ds} } \right] = \exp \left[ { – \int\limits_0^{10} {\left( {\frac{1}{{100 + s}}} \right)ds} } \right]}\)
misal \({u = 100 + s \Leftrightarrow du = ds}\)
\({}_{10}{p_{35}} = \exp \left[ { – \int\limits_{100}^{110} {\left( {\frac{1}{u}} \right)ds} } \right]\)
\({}_{10}{p_{35}} = \exp \left[ { – \ln \left( {110} \right) + \ln \left( {100} \right)} \right]\)
\({}_{10}{p_{35}} = \frac{{10}}{{11}}\) |
| Jawaban |
d. \(\frac{{10}}{{11}}\) |
