Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
April 2019 |
| Nomor Soal |
: |
16 |
SOAL
Diberikan:
\({\mu _x} = \left\{ {\begin{array}{*{20}{c}} {0,04} {, 0 < x < 40}\\ {0,05} {,x \ge 40} \end{array}} \right.\)
Tentukan nilai \(e_{25:\overline {25|} }^0\)
- 15,6
- 15,2
- 14,8
- 14,4
- 14,0
| Diketahui |
\({\mu _x} = \left\{ {\begin{array}{*{20}{c}} {0,04} {, 0 < x < 40}\\ {0,05} {,x \ge 40} \end{array}} \right.\) |
| Rumus yang digunakan |
\(e_{x:\overline {\left. {m + n} \right|} }^0 = e_{x:\overline {\left. m \right|} }^0 + {}_m{p_x} \cdot e_{x + m:\overline {\left. n \right|} }^0\)
\({}_t{p_x} = \exp \left( { – \int\limits_0^t {{\mu _x}\left( t \right)dt} } \right)\)
\(e_{x:\bar n|}^0 = \int\limits_0^n {{}_t{p_x}} dt\) |
| Proses pengerjaan |
\(e_{x:\overline {\left. {m + n} \right|} }^0 = e_{x:\overline {\left. m \right|} }^0 + {}_m{p_x} \cdot e_{x + m:\overline {\left. n \right|} }^0\)
\(e_{25:\overline {\left. {25} \right|} }^0 = e_{25:\overline {\left. {15} \right|} }^0 + {}_{15}{p_{25}} \cdot e_{40:\overline {\left. {10} \right|} }^0\)
\(= \int\limits_0^{15} {\exp \left( { – 0,04t} \right)dt} + \exp \left( { – 0,04 \cdot 15} \right) \cdot \int\limits_0^{10} {\exp \left( { – 0,05t} \right)dt} \)
\(= 11,279709 + 0,548812\left( {7,869387} \right)\)
\(= 15,59852\) |
| Jawaban |
a. 15,6 |
