Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Untuk (x) dan (y) dengan “independent future lifetimes” diberikan sebagai berikut:
- \({\bar a_x} = 10,06\)
- \({\bar a_y} = 11,95\)
- \({\bar a_{\overline {xy} }} = 12,59\)
- \({\bar A_{x\mathop y\limits^1 }} = 0,09\)
- \(\delta = 0,07\)
Hitunglah \({\bar A_{\mathop x\limits^1 y}}\)
- 0,15
- 0,20
- 0,25
- 0,30
- 0,35
| Rumus | \({\bar A_{\mathop x\limits^1 y}} = {\bar A_{xy}} – {A_{x\mathop y\limits^1 }}\) |
| Step 1 | \({\bar a_{xy}} = {\bar a_x} + {\bar a_y} – {\bar a_{\overline {xy} }}\) \({\bar a_{xy}} = 10,06 + 11,95 – 12,59\) \({\bar a_{xy}} = 9,42\) |
| \({\bar A_{xy}} = 1 – \delta {\bar a_{xy}}\) \({\bar A_{xy}} = 1 – 0,07\left( {9,42} \right)\) \({\bar A_{xy}} = 0,3406\) | |
| Step 2 | \({\bar A_{\mathop x\limits^1 y}} = {\bar A_{xy}} – {A_{x\mathop y\limits^1 }}\) \({\bar A_{\mathop x\limits^1 y}} = 0,3406 – 0,09\) \({\bar A_{\mathop x\limits^1 y}} = 0,2506\) \({\bar A_{\mathop x\limits^1 y}} \cong 0,25\) |
| Jawaban | c. \(0,25\) |