Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Berdasarkan soal nomor 23. Hitunglah \(Cov\left( {{T_{30:50}},{T_{\overline {30:50} }}} \right)\)
- 10
- 25
- 50
- 100
- 200
| Diketahui |
|
| 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 |