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 |