Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
Juni 2015 |
| Nomor Soal |
: |
26 |
SOAL
Berdasarkan soal nomor 23. Hitunglah \(Cov\left( {{T_{30:50}},{T_{\overline {30:50} }}} \right)\)
- 10
- 25
- 50
- 100
- 200
| Diketahui |
- \(\left( {30} \right)\) dan \(\left( {50} \right)\) adalah suatu independent lives dengan constant force of mortality, \(\mu = 0,05\)
- \(\delta = 0,03\)
|
| Rumus yang digunakan |
\(Cov\left( {{T_{xy}},{T_{\overline {xy} }}} \right) = \left( {e_x^0 – e_{xy}^0} \right)\left( {e_y^0 – e_{xy}^0} \right)\)
Untuk Distribusi Eksponensial: \(e_x^0 = \frac{1}{{{\mu _x}}}\) |
| Proses pengerjaan |
\(e_x^0 = e_y^0 = \frac{1}{{{\mu _x}}} = \frac{1}{{0.05}} = 20\)
\(e_{xy}^0 = \frac{1}{{{\mu _{xy}}}} = \frac{1}{{{\mu _x} + {\mu _x}}} = \frac{1}{{0.05 + 0.05}} = \frac{1}{{0.1}} = 10\) |
|
\(Cov\left( {{T_{xy}},{T_{\overline {xy} }}} \right) = \left( {e_x^0 – e_{xy}^0} \right)\left( {e_y^0 – e_{xy}^0} \right)\)
\(Cov\left( {{T_{xy}},{T_{\overline {xy} }}} \right) = \left( {20 – 10} \right)\left( {20 – 10} \right)\)
\(Cov\left( {{T_{xy}},{T_{\overline {xy} }}} \right) = 100\) |
| Jawaban |
d. 100 |
