Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
Juni 2016 |
| Nomor Soal |
: |
11 |
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. \(0,25\) |
