Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Untuk (x) dan (y) dengan “independent future lifetimes” diberikan sebagai berikut:
- \({\bar a_x} = 10,06\)
- \({\bar a_y} = 11,95\)
- \({\bar a_{\bar x\bar y}} = 12,59\)
- \({\bar A_{x\mathop y\limits^| }} = 0,04\)
- \(\delta = 0,07\)
Hitunglah \({A_{\mathop x\limits^| y}}\)
- 0,15
- 0,20
- 0,25
- 0,30
- 0,35
PEMBAHASAN
| Rumus | \({\bar A_{\mathop x\limits^| y}} + {\bar A_{x\mathop y\limits^| }} = {\bar A_{xy}}\) |
| Step 1 | \({\bar A_{xy}} = 1 – \delta {\bar a_{xy}}\) \({\bar a_x} + {\bar a_y} = {\bar a_{xy}} + {\bar a_{\bar x\bar y}}\) \(10,06 + 11,95 = {\bar a_{xy}} + 12,59\) \({\bar a_{xy}} = 9,42\) \({\bar A_{xy}} = 1 – 0,07(9,42)\) \({\bar A_{xy}} = 0,3406\) |
| Step 2 | \({\bar A_{\mathop x\limits^| y}} = {\bar A_{xy}} – {\bar A_{x\mathop y\limits^| }}\) \({\bar A_{\mathop x\limits^| y}} = 0,3406 – 0,04\) \({\bar A_{\mathop x\limits^| y}} = 0,3006\) \({\bar A_{\mathop x\limits^| y}} \cong 0,30\) |
| Jawaban | d. 0,30 |