Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
November 2018 |
| Nomor Soal |
: |
9 |
SOAL
Perhatikan fungsi survival berikut:
\({S_0}(x) = {\left( {1 – \frac{x}{{60}}} \right)^{\frac{1}{3}}},0 \le x \le 60\)
Berapakah \({\mu _{35}}?\)
- 0,0201
- 0,0167
- 0,0133
- 0,0067
- 0,0023
| Maka |
\({\mu _x} = \frac{{ – \frac{d}{{dt}}S(x)}}{{S(x)}}\)
\({\mu _x} = \frac{{ – \frac{d}{{dt}}{{\left( {1 – \frac{x}{{60}}} \right)}^{\frac{1}{3}}}}}{{{{\left( {1 – \frac{x}{{60}}} \right)}^{\frac{1}{3}}}}}\)
\({\mu _x} = \frac{{ – \frac{1}{3}\left( { – \frac{1}{{60}}} \right){{\left( {1 – \frac{x}{{60}}} \right)}^{ – \frac{2}{3}}}}}{{{{\left( {1 – \frac{x}{{60}}} \right)}^{\frac{1}{3}}}}}\) |
|
\({\mu _{35}} = \frac{{ – \frac{1}{3}\left( { – \frac{1}{{60}}} \right){{\left( {1 – \frac{{35}}{{60}}} \right)}^{ – \frac{2}{3}}}}}{{{{\left( {1 – \frac{{35}}{{60}}} \right)}^{\frac{1}{3}}}}}\)
\({\mu _{35}} = \frac{1}{{75}}\)
\({\mu _{35}} \cong 0,0133\) |
| Jawaban |
c. 0,0133 |
