Pembahasan Soal Ujian Profesi Aktuaris
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 |