Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
November 2016 |
| Nomor Soal |
: |
27 |
SOAL
Diketaui:
- \({\mu _X} = F + {e^{2x}},{\rm{ }}x \ge 0\)
- \(_{0.4}{p_0} = 0.45\)
Hitunglah niai F (dibulatkan)
- 0,2
- 0,3
- 0,46
- 0,52
- 0,63
| Diketahui |
- \({\mu _X} = F + {e^{2x}},{\rm{ }}x \ge 0\)
- \(_{0.4}{p_0} = 0.45\)
|
| Rumus yang digunakan |
\(_n{P_x} = \exp ( – \int\limits_x^{x + n} {{\mu _x}} dx)\) |
| Proses Pengerjaan |
\(_{0.4}{P_0} = \exp ( – \int\limits_0^{0.4} {F + {e^{2x}}{\rm{ }}} dx) = 0.45\)
selanjutnya
\(\exp ( – \int\limits_0^{0.4} {F + {e^{2x}}{\rm{ }}} dx) = 0.45\)
\(\Leftrightarrow \exp ( – 0.4F – 0.6128) = 0.45\)
\(\Leftrightarrow \ln (\exp ( – 0.4F – 0.6128)) = \ln (0.45)\)
\(\Leftrightarrow – 0.4F – 0.6128 = – 0.79851\)
\(\Leftrightarrow F = 0.46427\)
\(\Leftrightarrow F = 0.46\) |
| Jawaban |
c. 0.46 |
